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\(1^\text{st}\)-moment of the mass

Definition MYMACalc3 Review of Center of Mass of a Bar ,\MYMACalc3\Part III - Integrals\RectInt\2DAppsCM.html

3 Multiple Integrals in Rectangular Coordinates: Review of Center of Mass of a Bar

(\(2\)-sided) limit

Definition MYMACalc1 2-Sided Limits and Continuity,\MYMACalc1\Part II - Limits and Continuity\Intuitive\LimCont.html

1 Intuitive Limits and Continuity: 2-Sided Limits and Continuity

(\(2\)-sided) limit

Definition MYMACalc3 Intuitive Limits for Functions of 1 Variable (Review),\MYMACalc3\Part II - Derivatives\LimCont\Lim_1D.html

3 Limits and Continuity: Intuitive Limits for Functions of 1 Variable (Review)

(\(2\)-sided\)) limit is negative infinity

Definition MYMACalc1 2-Sided Limits and Continuity,\MYMACalc1\Part II - Limits and Continuity\Intuitive\LimCont.html

1 Intuitive Limits and Continuity: 2-Sided Limits and Continuity

(\(2\)-sided\)) limit is positive infinity

Definition MYMACalc1 2-Sided Limits and Continuity,\MYMACalc1\Part II - Limits and Continuity\Intuitive\LimCont.html

1 Intuitive Limits and Continuity: 2-Sided Limits and Continuity

(\(2\)-sided\)) limit is negative infinity

Definition MYMACalc3 When Limits Do Not Exist,\MYMACalc3\Part II - Derivatives\LimCont\Lim_1D.html

3 Limits and Continuity: When Limits Do Not Exist

(\(2\)-sided\)) limit is positive infinity

Definition MYMACalc3 When Limits Do Not Exist,\MYMACalc3\Part II - Derivatives\LimCont\Lim_1D.html

3 Limits and Continuity: When Limits Do Not Exist

2D Stokes' Theorem

Theorem MYMACalc3 Alternate Notations - 2D Stokes' Theorem,\MYMACalc3\Part IV - Theorems\ThmGreen\2DStokes.html,undefined,\MYMACalc3\Part IV - Theorems\ThmGreen\ApplCirc.html

3 Green's Theorem: Alternate Notations - 2D Stokes' Theorem

2D Gauss' Theorem

Theorem MYMACalc3 Alternate Notations - 2D Gauss' Theorem,\MYMACalc3\Part IV - Theorems\ThmGreen\2DGauss.html

3 Green's Theorem: Alternate Notations - 2D Gauss' Theorem

4D Cylindrical Coordinates

Definition MYMACalc3 Cylindrical and Spherical Coordinates in Higher Dimensions (Optional),\MYMACalc3\Part I - Geometry & Vectors\Coords\nDCylSphCoord.html

3 Coordinate Systems: Cylindrical and Spherical Coordinates in Higher Dimensions (Optional)

4D Spherical Coordinates

Definition MYMACalc3 Cylindrical and Spherical Coordinates in Higher Dimensions (Optional),\MYMACalc3\Part I - Geometry & Vectors\Coords\nDCylSphCoord.html

3 Coordinate Systems: Cylindrical and Spherical Coordinates in Higher Dimensions (Optional)

4-volume

Definition MYMACalc3 Riemann Sum Definition of Triple Integrals,\MYMACalc3\Part III - Integrals\RiemInt\3DRiem.html

3 Multiple Integrals as Riemann Sums: Riemann Sum Definition of Triple Integrals

A Vector Potential is Unique up to a Curl-Free Field

Theorem MYMACalc3 Finding Vector Potentials,\MYMACalc3\Part II - Derivatives\DivCurlPots\VecPots.html

3 Divergence, Curl and Potentials: Finding Vector Potentials

A Scalar Potential is Unique up to a Constant

Theorem MYMACalc3 Finding Scalar Potentials,\MYMACalc3\Part II - Derivatives\DivCurlPots\ScalPots.html

3 Divergence, Curl and Potentials: Finding Scalar Potentials

Absolute Value of the Triple Product

Theorem MYMACalc3 Geometric Interpretation of Triple Products,\MYMACalc3\Part I - Geometry & Vectors\Cross\TripleGeom.html

3 Cross Product: Geometric Interpretation of Triple Products

absolute minimum

3 Functions of Several Variables: Functions of \(1\) Variable

3 Max-Min Problems: Functions of \(2\) Variables

absolute maximum

3 Functions of Several Variables: Functions of \(1\) Variable

3 Max-Min Problems: Functions of \(2\) Variables

absolutely convergent

Definition MYMACalc2 The Absolute Convergence Test,\MYMACalc2\Part IV - Sequences & Series\SerGen\Abs.html,Overview,\MYMACalc2\Part IV - Sequences & Series\SerGen\Overview.html

2 Convergence of General Series: The Absolute Convergence Test

Definition MYMACalc3 Lines in \(\mathbb{R}^2\) - More on the Normal Equation,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\LineNonParam3.html,Lines - Parametric Equations,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\LineParam1.html,Planes in \(\mathbb{R}^3\) - More on the Normal Equation,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\PlaneNonParam2.html,Planes - Parametric Equations,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\PlaneParam1.html

3 Lines and Planes: Lines in \(\mathbb{R}^2\) - More on the Normal Equation

abstract form

Definition MYMACalc1 Parametric Lines,\MYMACalc1\Part I - Pre-Calculus\Vectors\Lines.html

1 Vectors: Parametric Lines

“abuse of notation”

Definition MYMACalc3 Derivative Along a Curve and the Gradient,\MYMACalc3\Part II - Derivatives\DirDerivGrad\DerCurve.html

3 Directional Derivatives and Gradients: Derivative Along a Curve and the Gradient

acceleration of gravity

Definition MYMACalc2 Falling near the Earth,\MYMACalc2\Part III - Differential Equations\DEApps\FreeFall.html

2 Applications of Differential Equations: Falling near the Earth

Add a Multiple of One Row to Another Row (Row Operation III)*

Theorem MYMACalc3 Properties of Determinants,\MYMACalc3\Part I - Geometry & Vectors\Cross\DetProp.html

3 Cross Product: Properties of Determinants

Addition and Subtraction of Power Series

Theorem MYMACalc2 Addition and Subtraction,\MYMACalc2\Part IV - Sequences & Series\PowSer\AddSub.html

2 Power Series: Addition and Subtraction

Additive

Theorem MYMACalc3 Properties of Determinants,\MYMACalc3\Part I - Geometry & Vectors\Cross\DetProp.html

3 Cross Product: Properties of Determinants

alternating

Definition MYMACalc2 The Alternating Series Test,\MYMACalc2\Part IV - Sequences & Series\SerGen\Alt.html,The Alternating Series Test - Justification and Proof,\MYMACalc2\Part IV - Sequences & Series\SerGen\AltPf.html,Overview,\MYMACalc2\Part IV - Sequences & Series\SerGen\Overview.html

2 Convergence of General Series: The Alternating Series Test

alternating harmonic series

Definition MYMACalc2 The Alternating Series Test,\MYMACalc2\Part IV - Sequences & Series\SerGen\Alt.html

2 Convergence of General Series: The Alternating Series Test

alternating series bound on the error in the approximation

Definition MYMACalc2 Approximating the Series - Alternating Series Bound,\MYMACalc2\Part IV - Sequences & Series\SerGen\ApproxSerAltBnd.html

2 Convergence of General Series: Approximating the Series - Alternating Series Bound

angle between the lines

Definition MYMACalc3 Parallel or Intersecting Lines in \(\mathbb{R}^2\),\MYMACalc3\Part I - Geometry & Vectors\LinePlane\LinesIntersect1.html

3 Lines and Planes: Parallel or Intersecting Lines in \(\mathbb{R}^2\)

angle between the planes

Definition MYMACalc3 Parallel and Intersecting Planes,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\PlanesIntersect.html

3 Lines and Planes: Parallel and Intersecting Planes

angle \(\theta\) between the line and the plane

Definition MYMACalc3 Parallel and Intersecting Lines and Planes in \(\mathbb{R}^3\),\MYMACalc3\Part I - Geometry & Vectors\LinePlane\LinePlaneIntersect.html

3 Lines and Planes: Parallel and Intersecting Lines and Planes in \(\mathbb{R}^3\)

angle

Definition MYMACalc1 Angles,\MYMACalc1\Part I - Pre-Calculus\Vectors\Angles.html

1 Vectors: Angles

angle

Definition MYMACalc3 Angles,\MYMACalc3\Part I - Geometry & Vectors\Dot\Angles.html

3 Dot Product: Angles

angle between the lines

Definition MYMACalc1 Intersections of Lines,\MYMACalc1\Part I - Pre-Calculus\Vectors\LinesIntersect.html

1 Vectors: Intersections of Lines

angular velocity

Definition MYMACalc3 Application - Balancing Torques,\MYMACalc3\Part I - Geometry & Vectors\Cross\BalTorques.html

3 Cross Product: Application - Balancing Torques

angular acceleration

Definition MYMACalc2 Moment of Inertia - Bar with Non-Uniform Density,\MYMACalc2\Part II - Applications of Integration\Mass\MomInertia.html

2 Mass and Center of Mass: Moment of Inertia - Bar with Non-Uniform Density

angular acceleration

Definition MYMACalc3 Application - Balancing Torques,\MYMACalc3\Part I - Geometry & Vectors\Cross\BalTorques.html

3 Cross Product: Application - Balancing Torques

antiderivative

Definition MYMACalc2 Definition of Antiderivatives,\MYMACalc2\Part I - Techniques of Integration\AntiDer\Def.html

2 Antiderivatives: Definition of Antiderivatives

antiderivative

Definition MYMACalc3 Generalizing Antiderivatives,\MYMACalc3\Part II - Derivatives\DivCurlPots\AntiDer.html

3 Divergence, Curl and Potentials: Generalizing Antiderivatives

antiderivative

Definition MYMACalc1 Definition of Antiderivatives,\MYMACalc1\Part V - Integrals\AntiDer\Def.html

1 Antiderivatives: Definition of Antiderivatives

Antisymmetry (Row Operation I)*

Theorem MYMACalc3 Properties of Determinants,\MYMACalc3\Part I - Geometry & Vectors\Cross\DetProp.html

3 Cross Product: Properties of Determinants

application point

Definition MYMACalc3 Application - Balancing Torques,\MYMACalc3\Part I - Geometry & Vectors\Cross\BalTorques.html

3 Cross Product: Application - Balancing Torques

arbitrarily

Definition MYMACalc2 Precise Definiton of Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\PrecDef.html

2 Sequences: Precise Definiton of Limits

arbitrarily

Definition MYMACalc1 Precise Limits at Infinity,\MYMACalc1\Part II - Limits and Continuity\Precise\LimatInf.html

1 Precise Limits and Continuity: Precise Limits at Infinity

Arc Length of any Curve

Theorem MYMACalc2 Differential of Arc Length,\MYMACalc2\Part II - Applications of Integration\ArcSurf\ArcDiff.html

2 Arc Length and Surface Area: Differential of Arc Length

Arc Length of the Graph of a Pair of Functions in 3D

Theorem MYMACalc2 Arc Length - 3-Dimensional Space,\MYMACalc2\Part II - Applications of Integration\ArcSurf\Arc3D.html

2 Arc Length and Surface Area: Arc Length - 3-Dimensional Space

arc length

Definition MYMACalc3 Arc Length,\MYMACalc3\Part I - Geometry & Vectors\LineInt\ArcLength.html

3 Line Integrals: Arc Length

Arc Length of the Curve

Definition MYMACalc3 Arc Length, Arc Length Parameter, and Speed,\MYMACalc3\Part I - Geometry & Vectors\CurveProps\ArcLen.html

3 Properties of Curves: Arc Length, Arc Length Parameter, and Speed

arc length function

Definition MYMACalc3 Arc Length, Arc Length Parameter, and Speed,\MYMACalc3\Part I - Geometry & Vectors\CurveProps\sParam.html

3 Properties of Curves: Arc Length, Arc Length Parameter, and Speed

Arc Length of a Polar Curve

Theorem MYMACalc2 Arc Length of a Polar Graph,\MYMACalc2\Part II - Applications of Integration\Polar\ArcLength.html

2 Polar Coordinates: Arc Length of a Polar Graph

Arc Length of a Parametric Curve

Theorem MYMACalc2 Arc Length of a Parametric Curve,\MYMACalc2\Part II - Applications of Integration\ArcSurf\ArcParam.html

2 Arc Length and Surface Area: Arc Length of a Parametric Curve

Arc Length of a Parametric Curve in 3D

Theorem MYMACalc2 Arc Length - 3-Dimensional Space,\MYMACalc2\Part II - Applications of Integration\ArcSurf\Arc3D.html

2 Arc Length and Surface Area: Arc Length - 3-Dimensional Space

Arc Length of the Graph of a Function

Theorem MYMACalc2 Arc Length of the Graph of a Function,\MYMACalc2\Part II - Applications of Integration\ArcSurf\ArcGraph.html

2 Arc Length and Surface Area: Arc Length of the Graph of a Function

arc length

Definition MYMACalc2 Arc Length - 3-Dimensional Space,\MYMACalc2\Part II - Applications of Integration\ArcSurf\Arc3D.html,Arc Length of the Graph of a Function,\MYMACalc2\Part II - Applications of Integration\ArcSurf\ArcGraph.html,Arc Length of a Parametric Curve,\MYMACalc2\Part II - Applications of Integration\ArcSurf\ArcParam.html

2 Arc Length and Surface Area: Arc Length - 3-Dimensional Space

area under \(f(x)\) above the interval \([a,b]\)

Definition MYMACalc1 Area as an Antiderivative,\MYMACalc1\Part V - Integrals\AntiDer\AreaAD.html

1 Antiderivatives: Area as an Antiderivative

area

Definition MYMACalc3 Applications of Double Integrals - Centroid of a Region,\MYMACalc3\Part III - Integrals\RectInt\2DAppsCentroid.html

3 Multiple Integrals in Rectangular Coordinates: Applications of Double Integrals - Centroid of a Region

Area as a \(y\)-Integral

Theorem MYMACalc1 Area as a \(y\)-Integral,\MYMACalc1\Part V - Integrals\IntegAppl\Int_y.html

1 Applications of Integration: Area as a \(y\)-Integral

Area Between Two Curves

Theorem MYMACalc1 Area Between Two Curves,\MYMACalc1\Part V - Integrals\IntegAppl\Between.html

1 Applications of Integration: Area Between Two Curves

Area Below a Curve

Theorem MYMACalc1 Area Below a Curve,\MYMACalc1\Part V - Integrals\IntegAppl\Below.html

1 Applications of Integration: Area Below a Curve

area function for \(f(x)\)

Definition MYMACalc2 Area as Antiderivative,\MYMACalc2\Part I - Techniques of Integration\AntiDer\AreaAD.html

2 Antiderivatives: Area as Antiderivative

Area of a Triangle

Theorem MYMACalc3 Areas,\MYMACalc3\Part I - Geometry & Vectors\Cross\Area.html

3 Cross Product: Areas

Area of a Parallelogram

Theorem MYMACalc3 Areas,\MYMACalc3\Part I - Geometry & Vectors\Cross\Area.html

3 Cross Product: Areas

area function for \(f(x)\)

Definition MYMACalc1 Area as an Antiderivative,\MYMACalc1\Part V - Integrals\AntiDer\AreaAD.html

1 Antiderivatives: Area as an Antiderivative

Area of a Polar Rectangle

Theorem MYMACalc3 Polar Coordinates - Grid Cell,\MYMACalc3\Part III - Integrals\CurvInt\Polar-Grid.html

3 Multiple Integrals in Curvilinear Coordinates: Polar Coordinates - Grid Cell

Area under a Curve as an Integral

Theorem MYMACalc1 Riemann Sums and Areas,\MYMACalc1\Part V - Integrals\RiemSum\Def.html

1 Riemann Sums: Riemann Sums and Areas

area under \(f(x)\) above the interval \([a,b]\)

Definition MYMACalc2 Area as Antiderivative,\MYMACalc2\Part I - Techniques of Integration\AntiDer\AreaAD.html

2 Antiderivatives: Area as Antiderivative

area of a polar rectangle

Definition MYMACalc3 Polar Coordinates - Grid Cell,\MYMACalc3\Part III - Integrals\CurvInt\Polar-Grid.html

3 Multiple Integrals in Curvilinear Coordinates: Polar Coordinates - Grid Cell

Area Enclosed by a Polar Graph

Theorem MYMACalc2 Area Enclosed by a Polar Graph,\MYMACalc2\Part II - Applications of Integration\Polar\Area.html

2 Polar Coordinates: Area Enclosed by a Polar Graph

Area Between Two Curves

Theorem MYMACalc2 Area Between Two Curves,\MYMACalc2\Part II - Applications of Integration\Area\Betw.html

2 Area and Average Value: Area Between Two Curves

Area Between Polar Graph

Theorem MYMACalc2 Area Between Polar Graphs,\MYMACalc2\Part II - Applications of Integration\Polar\AreaBetween.html

2 Polar Coordinates: Area Between Polar Graphs

Area Below a Curve

Theorem MYMACalc2 Area Below a Curve,\MYMACalc2\Part II - Applications of Integration\Area\Below.html

2 Area and Average Value: Area Below a Curve

Area as a \(y\)-Integral

Theorem MYMACalc2 Area as a \(y\)-Integral,\MYMACalc2\Part II - Applications of Integration\Area\yInt.html

2 Area and Average Value: Area as a \(y\)-Integral

Area under a Curve as an Integral

Theorem MYMACalc2 Riemann Sums and Areas,\MYMACalc2\Part I - Techniques of Integration\RiemSum\Def.html

2 Riemann Sums: Riemann Sums and Areas

asymptotes

Definition MYMACalc3 Quadratic Curves - Part 1,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\CrvR2Quad1.html

3 Curves and Surfaces: Quadratic Curves - Part 1

asymptotic lines

Definition MYMACalc3 Quadratic Curves - Part 1,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\CrvR2Quad1.html

3 Curves and Surfaces: Quadratic Curves - Part 1

asymptotic cone

Definition MYMACalc3 Quadratic Surfaces - Part 1,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3Quad1.html

3 Curves and Surfaces: Quadratic Surfaces - Part 1

autonomous differential equations

Definition MYMACalc2 undefined,\MYMACalc2\Part III - Differential Equations\DEApps\Cooling.html

2 Applications of Differential Equations: undefined

Average Value and Area

Theorem MYMACalc2 Average Value and Area,\MYMACalc2\Part II - Applications of Integration\Area\AveRect.html

2 Area and Average Value: Average Value and Area

average value of a function

Definition MYMACalc1 Average Value of a Function,\MYMACalc1\Part V - Integrals\IntegAppl\Ave.html,undefined,\MYMACalc1\Part V - Integrals\IntegAppl\MVT.html

1 Applications of Integration: Average Value of a Function

average value of a function

Definition MYMACalc2 Average Value of a Function,\MYMACalc2\Part II - Applications of Integration\Area\Ave.html,undefined,\MYMACalc2\Part II - Applications of Integration\Area\MeanVal.html

2 Area and Average Value: Average Value of a Function

Average Value of a Function

Theorem MYMACalc2 Average Value of a Function,\MYMACalc2\Part II - Applications of Integration\Area\Ave.html

2 Area and Average Value: Average Value of a Function

Average Value of a Function

Theorem MYMACalc1 Average Value of a Function,\MYMACalc1\Part V - Integrals\IntegAppl\Ave.html

1 Applications of Integration: Average Value of a Function

average radius of the cone

Definition MYMACalc2 Area of a Surface of Revolution,\MYMACalc2\Part II - Applications of Integration\ArcSurf\SurfRev.html

2 Arc Length and Surface Area: Area of a Surface of Revolution

Average Value and Area

Theorem MYMACalc1 Average Value and Area,\MYMACalc1\Part V - Integrals\IntegAppl\AveRect.html

1 Applications of Integration: Average Value and Area

average value

Definition MYMACalc3 Average Value,\MYMACalc3\Part I - Geometry & Vectors\LineInt\Ave.html

3 Line Integrals: Average Value

axes

Definition MYMACalc3 2D Rectangular Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DRectCoord.html,3D Rectangular Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\3DRectCoord.html

3 Coordinate Systems: 2D Rectangular Coordinates

axis

Definition MYMACalc3 Quadratic Surfaces - Part 1,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3Quad1.html,Quadratic Surfaces - Part 2,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3Quad2.html

3 Curves and Surfaces: Quadratic Surfaces - Part 1

azimuthal angle

Definition MYMACalc3 3D Spherical Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\3DSphCoord.html

3 Coordinate Systems: 3D Spherical Coordinates

Balancing problems

Definition MYMACalc2 undefined,\MYMACalc2\Part III - Differential Equations\DEApps\Mixing.html

2 Applications of Differential Equations: undefined

Best Fit Parabola

Theorem MYMACalc2 Simpson's Rule,\MYMACalc2\Part I - Techniques of Integration\NumInt\Simp.html

2 Numerical Integration: Simpson's Rule

bounded

Definition MYMACalc2 Bounded Sequences,\MYMACalc2\Part IV - Sequences & Series\Seq\Bnd.html

2 Sequences: Bounded Sequences

Bounded, Monotonic Sequence Theorem

Theorem MYMACalc2 Bounded, Monotonic Sequence Theorem,\MYMACalc2\Part IV - Sequences & Series\Seq\BndMonoThm.html,Precise Bounded Monotonic Sequence Theorem,\MYMACalc2\Part IV - Sequences & Series\Seq\PrecBM.html

2 Sequences: Bounded, Monotonic Sequence Theorem

bounded above

Definition MYMACalc2 Bounded Sequences,\MYMACalc2\Part IV - Sequences & Series\Seq\Bnd.html

2 Sequences: Bounded Sequences

bounded below

Definition MYMACalc2 Bounded Sequences,\MYMACalc2\Part IV - Sequences & Series\Seq\Bnd.html

2 Sequences: Bounded Sequences

By inspection

Definition MYMACalc3 Finding Scalar Potentials,\MYMACalc3\Part II - Derivatives\DivCurlPots\ScalPots.html

3 Divergence, Curl and Potentials: Finding Scalar Potentials

Cartesian Coordinate System

Definition MYMACalc3 2D Rectangular Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DRectCoord.html

3 Coordinate Systems: 2D Rectangular Coordinates

case work

Definition MYMACalc3 Second Derivative Test - Examples,\MYMACalc3\Part II - Derivatives\MaxMin\SecondDerTest1.html

3 Max-Min Problems: Second Derivative Test - Examples

center

Definition MYMACalc2 What is a Power Series?,\MYMACalc2\Part IV - Sequences & Series\PowSer\Def.html

2 Power Series: What is a Power Series?

Center of Mass of a Bar with Non-Uniform Density

Theorem MYMACalc2 Center of Mass - Bar with Non-Uniform Density,\MYMACalc2\Part II - Applications of Integration\Mass\CMbar.html

2 Mass and Center of Mass: Center of Mass - Bar with Non-Uniform Density

center of mass

2 Mass and Center of Mass: Center of Mass - Bar with Non-Uniform Density

center of mass

Definition MYMACalc3 Mass, Center of Mass and Centroid,\MYMACalc3\Part I - Geometry & Vectors\LineInt\MassCM.html, Review of Center of Mass of a Bar ,\MYMACalc3\Part III - Integrals\RectInt\2DAppsCM.html,Applications of Double Integrals - Center of Mass,\MYMACalc3\Part III - Integrals\RectInt\2DAppsCM.html,Center of Mass,\MYMACalc3\Part III - Integrals\SurfInt\CM.html

3 Line Integrals: Mass, Center of Mass and Centroid

3 Multiple Integrals in Rectangular Coordinates: Review of Center of Mass of a Bar

3 Parametric Surfaces and Surface Integrals: Applications of Double Integrals - Center of Mass

Center of Mass for Discrete Masses

Theorem MYMACalc2 Center of Mass - Discrete Masses,\MYMACalc2\Part II - Applications of Integration\Mass\CMdiscrete.html

2 Mass and Center of Mass: Center of Mass - Discrete Masses

centroid

Definition MYMACalc3 Mass, Center of Mass and Centroid,\MYMACalc3\Part I - Geometry & Vectors\LineInt\MassCM.html,Applications of Double Integrals - Centroid of a Region,\MYMACalc3\Part III - Integrals\RectInt\2DAppsCentroid.html,Centroid,\MYMACalc3\Part III - Integrals\SurfInt\Centroid.html

3 Line Integrals: Mass, Center of Mass and Centroid

3 Multiple Integrals in Rectangular Coordinates: Applications of Double Integrals - Centroid of a Region

3 Parametric Surfaces and Surface Integrals: Centroid

Chain Rule for Functions with \(4\) Intermediate Variable

Theorem MYMACalc3 Chain Rule with More Intermediate Variables,\MYMACalc3\Part II - Derivatives\Chain\ChainRule3.html

3 Chain Rule: Chain Rule with More Intermediate Variables

Chain Rule for Functions of \(1\) Variable

Theorem MYMACalc1 Chain Rule,\MYMACalc1\Part III - Derivatives\Chain\Chain.html

1 Chain Rule & Implicit Differentiation: Chain Rule

Chain Rule for Functions of \(1\) Variable

Theorem MYMACalc3 Chain Rule with \(1\) Intermediate Variable,\MYMACalc3\Part II - Derivatives\Chain\ChainRule1.html

3 Chain Rule: Chain Rule with \(1\) Intermediate Variable

Chain Rule for Functions with \(2\) Intermediate Variables

Theorem MYMACalc3 Chain Rule with \(2\) Intermediate Variables,\MYMACalc3\Part II - Derivatives\Chain\ChainRule2.html

3 Chain Rule: Chain Rule with \(2\) Intermediate Variables

Chain Rule for Functions with \(2\) Intermediate and \(2\) Independent Variables

Theorem MYMACalc3 Chain Rule with More Independent Variables,\MYMACalc3\Part II - Derivatives\Chain\ChainRule4.html

3 Chain Rule: Chain Rule with More Independent Variables

Change Limits

Theorem MYMACalc2 Definite Integrals - Changing Limits,\MYMACalc2\Part I - Techniques of Integration\IntSubs\DefChLim.html

2 Integration by Substitution: Definite Integrals - Changing Limits

change of variables

Definition MYMACalc1 Indefinite Integrals,\MYMACalc1\Part V - Integrals\IntSubs\Indef.html

1 Integration by Substitution: Indefinite Integrals

change in the dependent variable

Definition MYMACalc3 Differentials with \(3\) or more Variables,\MYMACalc3\Part II - Derivatives\LinApprox\Diff3Var.html

3 Linear Approximation: Differentials with \(3\) or more Variables

change of position

Definition MYMACalc1 Displacements,\MYMACalc1\Part I - Pre-Calculus\Vectors\Disp.html

1 Vectors: Displacements

change of variables

Definition MYMACalc2 Indefinite Integrals,\MYMACalc2\Part I - Techniques of Integration\IntSubs\Indef.html

2 Integration by Substitution: Indefinite Integrals

change of position

Definition MYMACalc3 The Vector Between Two Points - Displacement,\MYMACalc3\Part I - Geometry & Vectors\Vectors\Disp.html

3 Vectors: The Vector Between Two Points - Displacement

changes in the independent variables

Definition MYMACalc3 Differentials with \(3\) or more Variables,\MYMACalc3\Part II - Derivatives\LinApprox\Diff3Var.html

3 Linear Approximation: Differentials with \(3\) or more Variables

Changing Limits in Integration by Substitution

Theorem MYMACalc1 Definite Integrals - Changing Limits,\MYMACalc1\Part V - Integrals\IntSubs\DefChLim.html

1 Integration by Substitution: Definite Integrals - Changing Limits

Changing Limits in Integration by Substitution

Theorem MYMACalc2 Definite Integrals - Changing Limits,\MYMACalc2\Part I - Techniques of Integration\IntSubs\DefChLim.html

2 Integration by Substitution: Definite Integrals - Changing Limits

changing limits

Definition MYMACalc2 Definite Integrals - Changing Limits,\MYMACalc2\Part I - Techniques of Integration\IntSubs\DefChLim.html

2 Integration by Substitution: Definite Integrals - Changing Limits

changing limits

Definition MYMACalc1 Definite Integrals - Changing Limits,\MYMACalc1\Part V - Integrals\IntSubs\DefChLim.html

1 Integration by Substitution: Definite Integrals - Changing Limits

charge density

Definition MYMACalc3 The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian,\MYMACalc3\Part II - Derivatives\DivCurlPots\OpDivGrad.html

3 Divergence, Curl and Potentials: The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian

circle

Definition MYMACalc3 Quadratic Curves - Part 1,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\CrvR2Quad1.html

3 Curves and Surfaces: Quadratic Curves - Part 1

circular cylinders

Definition MYMACalc3 Quadratic Surfaces - Part 2,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3Quad2.html

3 Curves and Surfaces: Quadratic Surfaces - Part 2

circulation of the fluid

Definition MYMACalc3 Flow and Circulation,\MYMACalc3\Part I - Geometry & Vectors\LineInt\FlowCirc.html

3 Line Integrals: Flow and Circulation

circulation of the vector field

Definition MYMACalc3 Flow and Circulation,\MYMACalc3\Part I - Geometry & Vectors\LineInt\FlowCirc.html

3 Line Integrals: Flow and Circulation

Clairaut's Theorem

Theorem MYMACalc3 Clairaut's Theorem,\MYMACalc3\Part II - Derivatives\Higher\Clairaut.html

3 Higher Order Derivatives: Clairaut's Theorem

coefficient of viscosity

Definition MYMACalc2 Falling with Air Resistance,\MYMACalc2\Part III - Differential Equations\DEApps\TermVel.html

2 Applications of Differential Equations: Falling with Air Resistance

coefficients

Definition MYMACalc2 What is a Power Series?,\MYMACalc2\Part IV - Sequences & Series\PowSer\Def.html

2 Power Series: What is a Power Series?

comparison series

Definition MYMACalc2 Overview,\MYMACalc2\Part IV - Sequences & Series\SerPos\Overview.html

2 Convergence of Positive Series: Overview

comparison bound on the error in the approximation

Definition MYMACalc2 Approximating the Series - Comparison Bounds,\MYMACalc2\Part IV - Sequences & Series\SerPos\ApproxSerCompBnd.html

2 Convergence of Positive Series: Approximating the Series - Comparison Bounds

Comparison Test

Theorem MYMACalc2 Integrals Improper at a Finite Endpoint - Comparison Test,\MYMACalc2\Part I - Techniques of Integration\Improper\FinComp.html,Integrals Improper at an Infinite Endpoint - Comparison Test,\MYMACalc2\Part I - Techniques of Integration\Improper\InfComp.html

2 Improper Integrals: Integrals Improper at a Finite Endpoint - Comparison Test

complete surface

Definition MYMACalc3 The Theorem,\MYMACalc3\Part IV - Theorems\ThmGauss\Theorem.html

3 Gauss' Theorem: The Theorem

complex conjugate

Definition MYMACalc2 Complex Methods (Optional),\MYMACalc2\Part I - Techniques of Integration\ParFrac\Coeffs2Complex.html

2 Partial Fractions: Complex Methods (Optional)

component or scalar projection of \(\vec v\) perpenducular to \(\vec u\)

Definition MYMACalc1 Scalar Projections,\MYMACalc1\Part I - Pre-Calculus\Vectors\ProjScalar.html

1 Vectors: Scalar Projections

component or scalar projection of the vector \(\vec v\) parallel to the direction of \(\vec u\)

Definition MYMACalc3 Scalar Projections,\MYMACalc3\Part I - Geometry & Vectors\Dot\ProjScalar.html

3 Dot Product: Scalar Projections

component functions

Definition MYMACalc3 Line Integrals of Vectors,\MYMACalc3\Part I - Geometry & Vectors\LineInt\VectorInt.html

3 Line Integrals: Line Integrals of Vectors

component form

Definition MYMACalc1 Parametric Lines,\MYMACalc1\Part I - Pre-Calculus\Vectors\Lines.html

1 Vectors: Parametric Lines

component or scalar projection of \(\vec v\) parallel to \(\vec u\)

Definition MYMACalc1 Scalar Projections,\MYMACalc1\Part I - Pre-Calculus\Vectors\ProjScalar.html

1 Vectors: Scalar Projections

component or scalar projection of the vector \(\vec v\) parallel to the direction of \(\vec u\)

Definition MYMACalc1 Scalar Projections,\MYMACalc1\Part I - Pre-Calculus\Vectors\ProjScalar.html

1 Vectors: Scalar Projections

component or scalar projection of the vector \(\vec v\) perpendicular to the direction of \(\vec u\)

Definition MYMACalc3 Scalar Projections,\MYMACalc3\Part I - Geometry & Vectors\Dot\ProjScalar.html

3 Dot Product: Scalar Projections

component or scalar projection of \(\vec v\) perpenducular to \(\vec u\)

Definition MYMACalc3 Scalar Projections,\MYMACalc3\Part I - Geometry & Vectors\Dot\ProjScalar.html

3 Dot Product: Scalar Projections

component form

3 Lines and Planes: Lines in \(\mathbb{R}^2\) - More on the Normal Equation

component or scalar projection of the vector \(\vec v\) perpendicular to the direction of \(\vec u\)

Definition MYMACalc1 Scalar Projections,\MYMACalc1\Part I - Pre-Calculus\Vectors\ProjScalar.html

1 Vectors: Scalar Projections

component or scalar projection of \(\vec v\) parallel to \(\vec u\)

Definition MYMACalc3 Scalar Projections,\MYMACalc3\Part I - Geometry & Vectors\Dot\ProjScalar.html

3 Dot Product: Scalar Projections

components

Definition MYMACalc1 Scalar Projections,\MYMACalc1\Part I - Pre-Calculus\Vectors\ProjScalar.html

1 Vectors: Scalar Projections

components

Definition MYMACalc3 Scalar Projections,\MYMACalc3\Part I - Geometry & Vectors\Dot\ProjScalar.html

3 Dot Product: Scalar Projections

composition of functions

Definition MYMACalc3 Composition of Functions,\MYMACalc3\Part II - Derivatives\Chain\CompFunc.html

3 Chain Rule: Composition of Functions

composition of functions

Definition MYMACalc1 Compositions,\MYMACalc1\Part III - Derivatives\Chain\Comp.html

1 Chain Rule & Implicit Differentiation: Compositions

compute an integral which is improper at one or more interior points

Definition MYMACalc2 Integrals Improper at an Interior Point,\MYMACalc2\Part I - Techniques of Integration\Improper\Interior.html

2 Improper Integrals: Integrals Improper at an Interior Point

compute an integral which is improper at a finite left endpoint

Definition MYMACalc2 Integrals Improper at a Finite Endpoint,\MYMACalc2\Part I - Techniques of Integration\Improper\Fin.html

2 Improper Integrals: Integrals Improper at a Finite Endpoint

compute an integral which is improper at positive infinity

Definition MYMACalc2 Integrals Improper at an Infinite Endpoint,\MYMACalc2\Part I - Techniques of Integration\Improper\Inf.html

2 Improper Integrals: Integrals Improper at an Infinite Endpoint

conditionally convergent

Definition MYMACalc2 The Absolute Convergence Test,\MYMACalc2\Part IV - Sequences & Series\SerGen\Abs.html,Overview,\MYMACalc2\Part IV - Sequences & Series\SerGen\Overview.html

2 Convergence of General Series: The Absolute Convergence Test

cone

Definition MYMACalc3 Quadratic Surfaces - Part 1,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3Quad1.html

3 Curves and Surfaces: Quadratic Surfaces - Part 1

conic sections

Definition MYMACalc3 undefined,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\CrvR2Quad1.html

3 Curves and Surfaces: undefined

conjugate

Definition MYMACalc2 Indeterminate Form \(\infty-\infty\),\MYMACalc2\Part IV - Sequences & Series\Seq\LimSubt.html

2 Sequences: Indeterminate Form \(\infty-\infty\)

conjugate

Definition MYMACalc1 Indeterminate Form \(\infty-\infty\),\MYMACalc1\Part II - Limits and Continuity\Compute\LimSubt.html

1 Sequences: Indeterminate Form \(\infty-\infty\)

conservative

Definition MYMACalc3 Non-Existence of a Scalar Potential,\MYMACalc3\Part II - Derivatives\DivCurlPots\NoScalPot.html

3 Divergence, Curl and Potentials: Non-Existence of a Scalar Potential

Constant Sequences

Theorem MYMACalc1 Limits of Special Functions,\MYMACalc1\Part II - Limits and Continuity\Compute\LimSpec.html,Limit Laws,\MYMACalc1\Part II - Limits and Continuity\Precise\LimLaws.html

1 Computing Limits: Limits of Special Functions

1 Precise Limits and Continuity: Limit Laws

constant of integration

Definition MYMACalc2 Separable Differential Equations --- Example 7,\MYMACalc2\Part III - Differential Equations\DEIVP\esep7.html,Indefinite Integrals,\MYMACalc2\Part I - Techniques of Integration\RiemSum\IndefInt.html

2 Differential Equations and Initial Value Problems: Separable Differential Equations --- Example 7

2 Riemann Sums: Indefinite Integrals

Constant Sequences

Theorem MYMACalc2 Special Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\LimSpec.html,Precise Special Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\PrecSpec.html

2 Sequences: Special Limits

constant

Definition MYMACalc2 Geometric Series - Finite,\MYMACalc2\Part IV - Sequences & Series\Ser\GeomFin.html

2 Series: Geometric Series - Finite

constants of integration

Definition MYMACalc2 Solutions of Differential Equations,\MYMACalc2\Part III - Differential Equations\DEIVP\Sol.html

2 Differential Equations and Initial Value Problems: Solutions of Differential Equations

constraint equation

Definition MYMACalc3 Constrained Max-Min Problems,\MYMACalc3\Part II - Derivatives\MaxMin\Constraint.html

3 Max-Min Problems: Constrained Max-Min Problems

continuous from the right

Definition MYMACalc3 Intuitive Limits for Functions of 1 Variable (Review),\MYMACalc3\Part II - Derivatives\LimCont\Lim_1D.html

3 Limits and Continuity: Intuitive Limits for Functions of 1 Variable (Review)

continuous on a region

Definition MYMACalc3 Continuity,\MYMACalc3\Part II - Derivatives\LimCont\Continuity.html

3 Limits and Continuity: Continuity

continuous from the left

Definition MYMACalc3 Intuitive Limits for Functions of 1 Variable (Review),\MYMACalc3\Part II - Derivatives\LimCont\Lim_1D.html

3 Limits and Continuity: Intuitive Limits for Functions of 1 Variable (Review)

continuous from the left

Definition MYMACalc1 2-Sided Limits and Continuity,\MYMACalc1\Part II - Limits and Continuity\Intuitive\LimCont.html

1 Intuitive Limits and Continuity: 2-Sided Limits and Continuity

continuous

Definition MYMACalc3 Continuity,\MYMACalc3\Part II - Derivatives\LimCont\Continuity.html,Intuitive Limits for Functions of 1 Variable (Review),\MYMACalc3\Part II - Derivatives\LimCont\Lim_1D.html

3 Limits and Continuity: Continuity

continuous from the right

Definition MYMACalc1 2-Sided Limits and Continuity,\MYMACalc1\Part II - Limits and Continuity\Intuitive\LimCont.html

1 Intuitive Limits and Continuity: 2-Sided Limits and Continuity

continuous

Definition MYMACalc1 2-Sided Limits and Continuity,\MYMACalc1\Part II - Limits and Continuity\Intuitive\LimCont.html

1 Intuitive Limits and Continuity: 2-Sided Limits and Continuity

contour

Definition MYMACalc3 Level Sets and Contour Plots,\MYMACalc3\Part I - Geometry & Vectors\Functions\ContPlot3.html

3 Functions of Several Variables: Level Sets and Contour Plots

contour plot

Definition MYMACalc3 Level Sets and Contour Plots,\MYMACalc3\Part I - Geometry & Vectors\Functions\ContPlot3.html

3 Functions of Several Variables: Level Sets and Contour Plots

contractable

Definition MYMACalc3 Non-Existence of a Vector Potential,\MYMACalc3\Part II - Derivatives\DivCurlPots\NoVecPot.html

3 Divergence, Curl and Potentials: Non-Existence of a Vector Potential

contracting

Definition MYMACalc3 Algebraic Definition of Divergence,\MYMACalc3\Part II - Derivatives\DivCurlPots\DivAlg.html

3 Divergence, Curl and Potentials: Algebraic Definition of Divergence

contraction of the fluid

Definition MYMACalc3 Expansion and Contraction,\MYMACalc3\Part I - Geometry & Vectors\LineInt\Expansion.html

3 Line Integrals: Expansion and Contraction

Convergence Test

Definition MYMACalc2 Exercises,\MYMACalc2\Part IV - Sequences & Series\SerPos\x.html

2 Convergence of General Series: Exercises

2 Convergence of Positive Series:

convergent

Definition MYMACalc1 Precise Limits at Infinity,\MYMACalc1\Part II - Limits and Continuity\Precise\LimatInf.html

1 Precise Limits and Continuity: Precise Limits at Infinity

convergent

Definition MYMACalc2 Limits - Definition,\MYMACalc2\Part IV - Sequences & Series\Seq\LimDef.html,Precise Definiton of Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\PrecDef.html

2 Sequences: Limits - Definition

converges

Definition MYMACalc1 Left and Right Limits,\MYMACalc1\Part II - Limits and Continuity\Intuitive\LRLims.html

1 Intuitive Limits and Continuity: Left and Right Limits

converges to

Definition MYMACalc2 Limits - Definition,\MYMACalc2\Part IV - Sequences & Series\Seq\LimDef.html,Precise Definiton of Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\PrecDef.html

2 Sequences: Limits - Definition

converges

Definition MYMACalc3 Intuitive Limits for Functions of 1 Variable (Review),\MYMACalc3\Part II - Derivatives\LimCont\Lim_1D.html

3 Limits and Continuity: Intuitive Limits for Functions of 1 Variable (Review)

converges to

Definition MYMACalc1 Precise Limits at Infinity,\MYMACalc1\Part II - Limits and Continuity\Precise\LimatInf.html

1 Precise Limits and Continuity: Precise Limits at Infinity

converges to \(S\)

Definition MYMACalc2 The Sum of a Series,\MYMACalc2\Part IV - Sequences & Series\Ser\Sum.html

2 Series: The Sum of a Series

converging

Definition MYMACalc3 Algebraic Definition of Divergence,\MYMACalc3\Part II - Derivatives\DivCurlPots\DivAlg.html

3 Divergence, Curl and Potentials: Algebraic Definition of Divergence

Converting Between Rectangular and Polar Coordinates

Theorem MYMACalc2 Converting Between Rectangular and Polar Coordinates,\MYMACalc2\Part II - Applications of Integration\Polar\Convert.html

2 Polar Coordinates: Converting Between Rectangular and Polar Coordinates

Converting Between Rectangular and Polar Coordinates

Theorem MYMACalc3 2D Converting between Rectangular and Polar,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DPolarConvert.html

3 Coordinate Systems: 2D Converting between Rectangular and Polar

convex hull

Definition MYMACalc3 Polar Coordinates - Applications,\MYMACalc3\Part III - Integrals\CurvInt\Polar-Appl.html

3 Multiple Integrals in Curvilinear Coordinates: Polar Coordinates - Applications

coordinate curve

Definition MYMACalc3 2D Polar Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DPolarCoord.html,3D Cylindrical Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\3DCylCoord.html,3D Spherical Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\3DSphCoord.html

3 Coordinate Systems: 2D Polar Coordinates

coordinate dimensions

Definition MYMACalc3 Polar Coordinates - Grid Cell,\MYMACalc3\Part III - Integrals\CurvInt\Polar-Grid.html

3 Multiple Integrals in Curvilinear Coordinates: Polar Coordinates - Grid Cell

coordinate curves

Definition MYMACalc3 Coordinate Curves and Tangent Vectors,\MYMACalc3\Part III - Integrals\SurfInt\TanVecs.html

3 Parametric Surfaces and Surface Integrals: Coordinate Curves and Tangent Vectors

coordinate tangent vectors,

Definition MYMACalc3 2D Curvilinear Coordinates - Grid Cell,\MYMACalc3\Part III - Integrals\CurvInt\2DCurv-Grid.html

3 Multiple Integrals in Curvilinear Coordinates: 2D Curvilinear Coordinates - Grid Cell

coordinate surface

Definition MYMACalc3 3D Cylindrical Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\3DCylCoord.html,3D Spherical Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\3DSphCoord.html

3 Coordinate Systems: 3D Cylindrical Coordinates

coordinate grid

3 Coordinate Systems: 2D Polar Coordinates

coordinate center

Definition MYMACalc3 Polar Coordinates - Grid Cell,\MYMACalc3\Part III - Integrals\CurvInt\Polar-Grid.html

3 Multiple Integrals in Curvilinear Coordinates: Polar Coordinates - Grid Cell

coordinates

Definition MYMACalc3 Surfaces in \(\mathbb{R}^3\),\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3.html,Position,\MYMACalc3\Part III - Integrals\SurfInt\PosPlots.html

3 Curves and Surfaces: Surfaces in \(\mathbb{R}^3\)

3 Parametric Surfaces and Surface Integrals: Position

Co-Planar Vectors

Theorem MYMACalc3 Geometric Interpretation of Triple Products,\MYMACalc3\Part I - Geometry & Vectors\Cross\TripleGeom.html

3 Cross Product: Geometric Interpretation of Triple Products

Coulomb's Law of Electrostatics

Definition MYMACalc3 The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian,\MYMACalc3\Part II - Derivatives\DivCurlPots\OpDivGrad.html

3 Divergence, Curl and Potentials: The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian

counterclockwise

Definition MYMACalc3 Surfaces whose Boundaries have Several Curves,\MYMACalc3\Part IV - Theorems\ThmStokes\Hole.html

3 Stokes' Theorem: Surfaces whose Boundaries have Several Curves

critical points

Definition MYMACalc3 Functions of \(2\) Variables,\MYMACalc3\Part I - Geometry & Vectors\Functions\MaxMinSaddle2.html,Local Minima, Local Maxima and Inflection Points of Functions of \(1\) Variable,\MYMACalc3\Part II - Derivatives\MaxMin\MinMaxInfl.html,Local Minima, Local Maxima and Saddle Points of Functions of \(2\) Variables,\MYMACalc3\Part II - Derivatives\MaxMin\MinMaxSaddle.html

3 Functions of Several Variables: Functions of \(2\) Variables

3 Max-Min Problems: Local Minima, Local Maxima and Inflection Points of Functions of \(1\) Variable

critical point

Definition MYMACalc3 Functions of \(1\) Variable,\MYMACalc3\Part I - Geometry & Vectors\Functions\MaxMinSaddle.html

3 Functions of Several Variables: Functions of \(1\) Variable

critical points

Definition MYMACalc1 \(2^\text{nd}\) Derivative Test,\MYMACalc1\Part IV - Applications of Derivatives\MaxMin\2ndDerivTest.html

1 Max/Min Problems: \(2^\text{nd}\) Derivative Test

cross

Definition MYMACalc3 Quadratic Curves - Part 1,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\CrvR2Quad1.html

3 Curves and Surfaces: Quadratic Curves - Part 1

cross product

Definition MYMACalc3 Algebraic Definition of Cross Products,\MYMACalc3\Part I - Geometry & Vectors\Cross\CrossAlg.html

3 Cross Product: Algebraic Definition of Cross Products

cubic

Definition MYMACalc2 What is a Differential Equation?,\MYMACalc2\Part III - Differential Equations\DEIVP\Def.html

2 Differential Equations and Initial Value Problems: What is a Differential Equation?

curl

Definition MYMACalc3 undefined,\MYMACalc3\Part II - Derivatives\DivCurlPots\DelOperator.html,The Del Operator,\MYMACalc3\Part II - Derivatives\DivCurlPots\DelOperator.html,Algebraic Definition of Curl,\MYMACalc3\Part II - Derivatives\DivCurlPots\CurlAlg.html

3 Divergence, Curl and Potentials: undefined

Curl of a Gradient Identity

Theorem MYMACalc3 The Curl of a Gradient (\(\vec\nabla\times\vec\nabla f\)),\MYMACalc3\Part II - Derivatives\DivCurlPots\OpCurlGrad.html

3 Divergence, Curl and Potentials: The Curl of a Gradient (\(\vec\nabla\times\vec\nabla f\))

curl field

Definition MYMACalc3 Non-Existence of a Vector Potential,\MYMACalc3\Part II - Derivatives\DivCurlPots\NoVecPot.html

3 Divergence, Curl and Potentials: Non-Existence of a Vector Potential

curl-free

Definition MYMACalc3 Algebraic Definition of Curl,\MYMACalc3\Part II - Derivatives\DivCurlPots\CurlAlg.html,Non-Existence of a Scalar Potential,\MYMACalc3\Part II - Derivatives\DivCurlPots\NoScalPot.html

3 Divergence, Curl and Potentials: Algebraic Definition of Curl

curly d

Definition MYMACalc3 Computation,\MYMACalc3\Part II - Derivatives\ParDerTanPlane\Compute.html

3 Partial Derivatives and Tangent Planes: Computation

curvature

Definition MYMACalc3 Curvature,\MYMACalc3\Part I - Geometry & Vectors\CurveProps\Curvature.html

3 Properties of Curves: Curvature

curve

Definition MYMACalc1 Parametric Curves,\MYMACalc1\Part I - Pre-Calculus\Vectors\Curves.html

1 Vectors: Parametric Curves

curve

Definition MYMACalc3 Curves in \(\mathbb{R}^2\),\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\CrvR2.html

3 Curves and Surfaces: Curves in \(\mathbb{R}^2\)

curvilinear rectangle

Definition MYMACalc3 2D Curvilinear Coordinates - Grid Cell Area,\MYMACalc3\Part III - Integrals\CurvInt\2DCurv-GridArea.html

3 Multiple Integrals in Curvilinear Coordinates: 2D Curvilinear Coordinates - Grid Cell Area

curvilinear coordinate system

Definition MYMACalc3 Introduction to Parametric Surfaces,\MYMACalc3\Part III - Integrals\SurfInt\PosPlots.html,Position,\MYMACalc3\Part III - Integrals\SurfInt\PosPlots.html

3 Parametric Surfaces and Surface Integrals: Introduction to Parametric Surfaces

curvilinear coordinates

Definition MYMACalc3 2D Curvilinear Coordinates - Grid Cell,\MYMACalc3\Part III - Integrals\CurvInt\2DCurv-Grid.html

3 Multiple Integrals in Curvilinear Coordinates: 2D Curvilinear Coordinates - Grid Cell

cusp

Definition MYMACalc1 Parametric Curves,\MYMACalc1\Part I - Pre-Calculus\Vectors\Curves.html

1 Vectors: Parametric Curves

cusp

Definition MYMACalc2 Arc Length of a Parametric Curve,\MYMACalc2\Part II - Applications of Integration\ArcSurf\ArcParam.html

2 Arc Length and Surface Area: Arc Length of a Parametric Curve

cusp

Definition MYMACalc3 Curves in \(\mathbb{R}^2\),\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\CrvR2.html

3 Curves and Surfaces: Curves in \(\mathbb{R}^2\)

cylinder

Definition MYMACalc3 Quadratic Surfaces - Part 2,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3Quad2.html

3 Curves and Surfaces: Quadratic Surfaces - Part 2

Cylindrical Coordinates

Definition MYMACalc3 3D Cylindrical Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\3DCylCoord.html

3 Coordinate Systems: 3D Cylindrical Coordinates

cylindrical shells

Definition MYMACalc2 Solids of Revolution,\MYMACalc2\Part II - Applications of Integration\Vol\Rev.html

2 Volume: Solids of Revolution

decreasing

Definition MYMACalc2 Monotonic Sequences,\MYMACalc2\Part IV - Sequences & Series\Seq\Mono.html

2 Sequences: Monotonic Sequences

decreasing in absolute value

2 Convergence of General Series: The Alternating Series Test

defined recursively

Definition MYMACalc2 Recursively Defined Sequences,\MYMACalc2\Part IV - Sequences & Series\Seq\Recur.html

2 Sequences: Recursively Defined Sequences

(definite) integral

Definition MYMACalc2 Riemann Sums and Areas,\MYMACalc2\Part I - Techniques of Integration\RiemSum\Def.html,Riemann Sums and Integrals (Optional),\MYMACalc2\Part I - Techniques of Integration\RiemSum\Def2.html

2 Riemann Sums: Riemann Sums and Areas

degree

Definition MYMACalc2 What is a Differential Equation?,\MYMACalc2\Part III - Differential Equations\DEIVP\Def.html

2 Differential Equations and Initial Value Problems: What is a Differential Equation?

-degree term

Definition MYMACalc2 What is a Power Series?,\MYMACalc2\Part IV - Sequences & Series\PowSer\Def.html

2 Power Series: What is a Power Series?

del operator

Definition MYMACalc3 undefined,\MYMACalc3\Part II - Derivatives\DivCurlPots\DelOperator.html,The Del Operator,\MYMACalc3\Part II - Derivatives\DivCurlPots\DelOperator.html

3 Divergence, Curl and Potentials: undefined

"del"

Definition MYMACalc3 Algebraic Definition of Partial Derivatives,\MYMACalc3\Part II - Derivatives\ParDerTanPlane\ParDerAlg.html

3 Partial Derivatives and Tangent Planes: Algebraic Definition of Partial Derivatives

"del".

Definition MYMACalc3 Derivative Along a Curve and the Gradient,\MYMACalc3\Part II - Derivatives\DirDerivGrad\DerCurve.html

3 Directional Derivatives and Gradients: Derivative Along a Curve and the Gradient

dependent variable

Definition MYMACalc2 What is a Differential Equation?,\MYMACalc2\Part III - Differential Equations\DEIVP\Def.html

2 Differential Equations and Initial Value Problems: What is a Differential Equation?

dependent

Definition MYMACalc3 Chain Rule with \(1\) Intermediate Variable,\MYMACalc3\Part II - Derivatives\Chain\ChainRule1.html

3 Chain Rule: Chain Rule with \(1\) Intermediate Variable

dependent

Definition MYMACalc1 Chain Rule,\MYMACalc1\Part III - Derivatives\Chain\Chain.html

1 Chain Rule & Implicit Differentiation: Chain Rule

dependent variable

Definition MYMACalc3 Formulas,\MYMACalc3\Part I - Geometry & Vectors\Functions\Formulas.html

3 Functions of Several Variables: Formulas

derivative of \(f(x,y)\) along \(\vec v\)

Definition MYMACalc3 Derivative Along a Vector,\MYMACalc3\Part II - Derivatives\DirDerivGrad\DerVec.html,Algebraic Definition of Partial Derivatives,\MYMACalc3\Part II - Derivatives\ParDerTanPlane\ParDerAlg.html

3 Directional Derivatives and Gradients: Derivative Along a Vector

3 Partial Derivatives and Tangent Planes: Algebraic Definition of Partial Derivatives

Derivative of the Area Function

Theorem MYMACalc2 Area as Antiderivative,\MYMACalc2\Part I - Techniques of Integration\AntiDer\AreaAD.html

2 Antiderivatives: Area as Antiderivative

Derivative along a Curve

Theorem MYMACalc3 Derivative Along a Vector,\MYMACalc3\Part II - Derivatives\DirDerivGrad\DerVec.html

3 Directional Derivatives and Gradients: Derivative Along a Vector

derivative of the function \(f\) along the curve \(\vec r(t)\)

Definition MYMACalc3 Derivative Along a Curve and the Gradient,\MYMACalc3\Part II - Derivatives\DirDerivGrad\DerCurve.html

3 Directional Derivatives and Gradients: Derivative Along a Curve and the Gradient

Derivative as a Function

Theorem MYMACalc1 Derivative as a Function,\MYMACalc1\Part III - Derivatives\DefTanLine\DerivFn.html

1 Definitions and Tangent Lines: Derivative as a Function

derivative of the function \(f(x)\)

Definition MYMACalc1 Derivative as a Function,\MYMACalc1\Part III - Derivatives\DefTanLine\DerivFn.html

1 Definitions and Tangent Lines: Derivative as a Function

Derivative of the Integral

Theorem MYMACalc2 The Fundamental Theorem of Calculus for Integrals,\MYMACalc2\Part I - Techniques of Integration\RiemSum\IntFTC.html

2 Riemann Sums: The Fundamental Theorem of Calculus for Integrals

Derivative of the Integral

Theorem MYMACalc1 The Fundamental Theorem of Calculus for Integrals,\MYMACalc1\Part V - Integrals\RiemSum\IntFTC.html

1 Riemann Sums: The Fundamental Theorem of Calculus for Integrals

derivative of a vector function

Definition MYMACalc3 Derivatives of Vector Functions,\MYMACalc3\Part I - Geometry & Vectors\CurveProps\Der.html

3 Properties of Curves: Derivatives of Vector Functions

Derivative along a Vector

Theorem MYMACalc3 Derivative Along a Vector,\MYMACalc3\Part II - Derivatives\DirDerivGrad\DerVec.html

3 Directional Derivatives and Gradients: Derivative Along a Vector

Derivative at a Point

Theorem MYMACalc1 Derivative at a Point,\MYMACalc1\Part III - Derivatives\DefTanLine\DerivPt.html

1 Definitions and Tangent Lines: Derivative at a Point

derivative of the function \(f(x)\) at the point \(x=a\)

Definition MYMACalc1 Derivative at a Point,\MYMACalc1\Part III - Derivatives\DefTanLine\DerivPt.html

1 Definitions and Tangent Lines: Derivative at a Point

derivative of a vector function

Definition MYMACalc1 Velocity Vector,\MYMACalc1\Part III - Derivatives\ParamCurves\Velocity.html

1 Parametric Curves: Velocity Vector

Derivative of the Area Function

Theorem MYMACalc1 Area as an Antiderivative,\MYMACalc1\Part V - Integrals\AntiDer\AreaAD.html

1 Antiderivatives: Area as an Antiderivative

determinant of a \(3\times3\) matrix

Definition MYMACalc3 Method of Diagonals,\MYMACalc3\Part I - Geometry & Vectors\Cross\DetDiag.html

3 Cross Product: Method of Diagonals

determinant of a \(2\times2\) matrix

Definition MYMACalc3 Method of Diagonals,\MYMACalc3\Part I - Geometry & Vectors\Cross\DetDiag.html

3 Cross Product: Method of Diagonals

difference (or change) in the independent variable

Definition MYMACalc3 Differentials with \(1\) Variable,\MYMACalc3\Part II - Derivatives\LinApprox\Diff1Var.html

3 Linear Approximation: Differentials with \(1\) Variable

difference (or change) in the dependent variable

Definition MYMACalc1 Differences,\MYMACalc1\Part III - Derivatives\DiffLinApprox\Differentials.html

1 Differentials & Linear Approximation: Differences

difference (or change) in the dependent variable

Definition MYMACalc3 Differentials with \(1\) Variable,\MYMACalc3\Part II - Derivatives\LinApprox\Diff1Var.html

3 Linear Approximation: Differentials with \(1\) Variable

difference (or change) in the independent variable

Definition MYMACalc1 Differences,\MYMACalc1\Part III - Derivatives\DiffLinApprox\Differentials.html

1 Differentials & Linear Approximation: Differences

difference (or change) in the independent variables

Definition MYMACalc3 Differentials with \(2\) Variables,\MYMACalc3\Part II - Derivatives\LinApprox\Diff2Var.html

3 Linear Approximation: Differentials with \(2\) Variables

difference (or change) in the dependent variable

Definition MYMACalc3 Differentials with \(2\) Variables,\MYMACalc3\Part II - Derivatives\LinApprox\Diff2Var.html

3 Linear Approximation: Differentials with \(2\) Variables

differential equation

Definition MYMACalc1 From Acceleration to Velocity and Position,\MYMACalc1\Part V - Integrals\AntiDer\AccVelPos.html

1 Antiderivatives: From Acceleration to Velocity and Position

differential of the dependent variable

Definition MYMACalc1 Differences,\MYMACalc1\Part III - Derivatives\DiffLinApprox\Differentials.html

1 Differentials & Linear Approximation: Differences

differential of arc length

Definition MYMACalc2 Differential of Arc Length,\MYMACalc2\Part II - Applications of Integration\ArcSurf\ArcDiff.html

2 Arc Length and Surface Area: Differential of Arc Length

differential notation

Definition MYMACalc3 Higher Derivatives,\MYMACalc3\Part II - Derivatives\Higher\HigherDer.html

3 Higher Order Derivatives: Higher Derivatives

differential of the independent variable

Definition MYMACalc3 Differentials with \(1\) Variable,\MYMACalc3\Part II - Derivatives\LinApprox\Diff1Var.html

3 Linear Approximation: Differentials with \(1\) Variable

differential of the dependent variable

Definition MYMACalc3 Differentials with \(1\) Variable,\MYMACalc3\Part II - Derivatives\LinApprox\Diff1Var.html,Differentials with \(2\) Variables,\MYMACalc3\Part II - Derivatives\LinApprox\Diff2Var.html,Differentials with \(3\) or more Variables,\MYMACalc3\Part II - Derivatives\LinApprox\Diff3Var.html

3 Linear Approximation: Differentials with \(1\) Variable

differential of the independent variable

Definition MYMACalc1 Differences,\MYMACalc1\Part III - Derivatives\DiffLinApprox\Differentials.html

1 Differentials & Linear Approximation: Differences

differential equation

Definition MYMACalc2 Differential Equations and Initial Value Problems,\MYMACalc2\Part I - Techniques of Integration\AntiDer\DiffEq.html

2 Antiderivatives: Differential Equations and Initial Value Problems

differentials of the independent variables

Definition MYMACalc3 Differentials with \(2\) Variables,\MYMACalc3\Part II - Derivatives\LinApprox\Diff2Var.html,Differentials with \(3\) or more Variables,\MYMACalc3\Part II - Derivatives\LinApprox\Diff3Var.html

3 Linear Approximation: Differentials with \(2\) Variables

Differentiation of Power Series

Theorem MYMACalc2 Differentiation,\MYMACalc2\Part IV - Sequences & Series\PowSer\Diff.html

2 Power Series: Differentiation

direct second partials

Definition MYMACalc3 Higher Derivatives,\MYMACalc3\Part II - Derivatives\Higher\HigherDer.html

3 Higher Order Derivatives: Higher Derivatives

direction

Definition MYMACalc3 Vectors as Arrows,\MYMACalc3\Part I - Geometry & Vectors\Vectors\Arrow.html,Direction,\MYMACalc3\Part I - Geometry & Vectors\Vectors\Dir.html

3 Vectors: Vectors as Arrows

direction

Definition MYMACalc1 Vectors as Arrows,\MYMACalc1\Part I - Pre-Calculus\Vectors\Arrow.html,Direction,\MYMACalc1\Part I - Pre-Calculus\Vectors\Dir.html

1 Vectors: Vectors as Arrows

direction cosines

Definition MYMACalc3 Direction,\MYMACalc3\Part I - Geometry & Vectors\Vectors\Dir.html

3 Vectors: Direction

direction cosines

Definition MYMACalc1 Direction,\MYMACalc1\Part I - Pre-Calculus\Vectors\Dir.html

1 Vectors: Direction

direction angles

Definition MYMACalc3 Direction,\MYMACalc3\Part I - Geometry & Vectors\Vectors\Dir.html

3 Vectors: Direction

direction angles

Definition MYMACalc1 Direction,\MYMACalc1\Part I - Pre-Calculus\Vectors\Dir.html

1 Vectors: Direction

directional derivative of \(f(x,y)\) along \(\vec v\)

Definition MYMACalc3 Directional Derivatives,\MYMACalc3\Part II - Derivatives\DirDerivGrad\DirecDeriv.html

3 Directional Derivatives and Gradients: Directional Derivatives

directional derivative of \(f(x,y)\) in the direction of \(\vec v\)

Definition MYMACalc3 Directional Derivatives,\MYMACalc3\Part II - Derivatives\DirDerivGrad\DirecDeriv.html

3 Directional Derivatives and Gradients: Directional Derivatives

discriminant

Definition MYMACalc3 Local Minima, Local Maxima and Saddle Points of Functions of \(2\) Variables,\MYMACalc3\Part II - Derivatives\MaxMin\MinMaxSaddle.html

3 Max-Min Problems: Local Minima, Local Maxima and Saddle Points of Functions of \(2\) Variables

displacement vector

Definition MYMACalc1 Displacements,\MYMACalc1\Part I - Pre-Calculus\Vectors\Disp.html

1 Vectors: Displacements

displacement

Definition MYMACalc1 Displacements,\MYMACalc1\Part I - Pre-Calculus\Vectors\Disp.html

1 Vectors: Displacements

displacement vector

Definition MYMACalc3 The Vector Between Two Points - Displacement,\MYMACalc3\Part I - Geometry & Vectors\Vectors\Disp.html

3 Vectors: The Vector Between Two Points - Displacement

displacement

Definition MYMACalc3 The Vector Between Two Points - Displacement,\MYMACalc3\Part I - Geometry & Vectors\Vectors\Disp.html

3 Vectors: The Vector Between Two Points - Displacement

Distance Formula in \(\mathbb{R}^3\)

Theorem MYMACalc3 Distance Formula in 3D,\MYMACalc3\Part I - Geometry & Vectors\Coords\3DDistance.html

3 Coordinate Systems: Distance Formula in 3D

Distance Formula in \(\mathbb{R}^n\)

Theorem MYMACalc3 Distance Formula in Higher Dimensions (Optional),\MYMACalc3\Part I - Geometry & Vectors\Coords\nDDistance.html

3 Coordinate Systems: Distance Formula in Higher Dimensions (Optional)

Distance from a Point to a Line in \(\mathbb{R}^2\)

Theorem MYMACalc3 Distance from a Point to a Line - \(\mathbb{R}^2\),\MYMACalc3\Part I - Geometry & Vectors\LinePlane\DistPoint2LineR2.html

3 Lines and Planes: Distance from a Point to a Line - \(\mathbb{R}^2\)

Distance from a Point to a Line

Theorem MYMACalc3 Distance from a Point to a Line - \(\mathbb{R}^3\),\MYMACalc3\Part I - Geometry & Vectors\LinePlane\DistPoint2LineR3.html

3 Lines and Planes: Distance from a Point to a Line - \(\mathbb{R}^3\)

Distance Formula

Theorem MYMACalc3 Distance Formula in 2D,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DDistance.html

3 Coordinate Systems: Distance Formula in 2D

Distance from a Point to a Plane

Theorem MYMACalc3 Distance from a Point to a Plane,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\DistPoint2Plane.html

3 Lines and Planes: Distance from a Point to a Plane

Distance from a Point to a Line in \(\mathbb{R}^3\)

Theorem MYMACalc3 Distance from a Point to a Line - \(\mathbb{R}^3\),\MYMACalc3\Part I - Geometry & Vectors\LinePlane\DistPoint2LineR3.html

3 Lines and Planes: Distance from a Point to a Line - \(\mathbb{R}^3\)

divergence

Definition MYMACalc3 undefined,\MYMACalc3\Part II - Derivatives\DivCurlPots\DelOperator.html,The Del Operator,\MYMACalc3\Part II - Derivatives\DivCurlPots\DelOperator.html,Algebraic Definition of Divergence,\MYMACalc3\Part II - Derivatives\DivCurlPots\DivAlg.html

3 Divergence, Curl and Potentials: undefined

Divergence of a Curl Identity

Theorem MYMACalc3 The Divergence of a Curl (\(\vec\nabla\cdot\vec\nabla\times\vec F\)),\MYMACalc3\Part II - Derivatives\DivCurlPots\OpDivCurl.html

3 Divergence, Curl and Potentials: The Divergence of a Curl (\(\vec\nabla\cdot\vec\nabla\times\vec F\))

divergence-free

Definition MYMACalc3 Algebraic Definition of Divergence,\MYMACalc3\Part II - Derivatives\DivCurlPots\DivAlg.html,Non-Existence of a Vector Potential,\MYMACalc3\Part II - Derivatives\DivCurlPots\NoVecPot.html

3 Divergence, Curl and Potentials: Algebraic Definition of Divergence

divergent

Definition MYMACalc1 Precise Limits at Infinity,\MYMACalc1\Part II - Limits and Continuity\Precise\LimatInf.html

1 Precise Limits and Continuity: Precise Limits at Infinity

divergent

Definition MYMACalc2 The Absolute Convergence Test,\MYMACalc2\Part IV - Sequences & Series\SerGen\Abs.html,Overview,\MYMACalc2\Part IV - Sequences & Series\SerGen\Overview.html,Limits - Definition,\MYMACalc2\Part IV - Sequences & Series\Seq\LimDef.html,Precise Definiton of Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\PrecDef.html,The Sum of a Series,\MYMACalc2\Part IV - Sequences & Series\Ser\Sum.html

2 Convergence of General Series: The Absolute Convergence Test

2 Sequences: Overview

2 Series: Limits - Definition

diverges

Definition MYMACalc1 Left and Right Limits,\MYMACalc1\Part II - Limits and Continuity\Intuitive\LRLims.html,Precise Limits at Infinity,\MYMACalc1\Part II - Limits and Continuity\Precise\LimatInf.html

1 Intuitive Limits and Continuity: Left and Right Limits

1 Precise Limits and Continuity: Precise Limits at Infinity

diverges to \(-\infty\)

Definition MYMACalc3 When Limits Do Not Exist,\MYMACalc3\Part II - Derivatives\LimCont\Lim_1D.html

3 Limits and Continuity: When Limits Do Not Exist

diverges to \(\infty\)

Definition MYMACalc3 When Limits Do Not Exist,\MYMACalc3\Part II - Derivatives\LimCont\Lim_1D.html

3 Limits and Continuity: When Limits Do Not Exist

diverges to \(-\infty\) on the left or right

Definition MYMACalc3 When Limits Do Not Exist,\MYMACalc3\Part II - Derivatives\LimCont\Lim_1D.html

3 Limits and Continuity: When Limits Do Not Exist

diverges

Definition MYMACalc2 Limits - Definition,\MYMACalc2\Part IV - Sequences & Series\Seq\LimDef.html,Precise Definiton of Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\PrecDef.html,The Sum of a Series,\MYMACalc2\Part IV - Sequences & Series\Ser\Sum.html

2 Sequences: Limits - Definition

2 Series: Precise Definiton of Limits

diverges to \(\infty\) on the left or right

Definition MYMACalc3 When Limits Do Not Exist,\MYMACalc3\Part II - Derivatives\LimCont\Lim_1D.html

3 Limits and Continuity: When Limits Do Not Exist

diverges to \(-\infty\)

Definition MYMACalc1 2-Sided Limits and Continuity,\MYMACalc1\Part II - Limits and Continuity\Intuitive\LimCont.html

1 Intuitive Limits and Continuity: 2-Sided Limits and Continuity

diverges

Definition MYMACalc3 Intuitive Limits for Functions of 1 Variable (Review),\MYMACalc3\Part II - Derivatives\LimCont\Lim_1D.html

3 Limits and Continuity: Intuitive Limits for Functions of 1 Variable (Review)

diverges to \(\infty\) on the left or right

Definition MYMACalc1 When Limits Do Not Exist,\MYMACalc1\Part II - Limits and Continuity\Intuitive\LRLims.html

1 Intuitive Limits and Continuity: When Limits Do Not Exist

diverges to positive infinity

Definition MYMACalc2 Limits - Definition,\MYMACalc2\Part IV - Sequences & Series\Seq\LimDef.html

2 Sequences: Limits - Definition

diverges to \(\infty\)

Definition MYMACalc1 2-Sided Limits and Continuity,\MYMACalc1\Part II - Limits and Continuity\Intuitive\LimCont.html

1 Intuitive Limits and Continuity: 2-Sided Limits and Continuity

diverges to \(-\infty\) on the left or right

Definition MYMACalc1 When Limits Do Not Exist,\MYMACalc1\Part II - Limits and Continuity\Intuitive\LRLims.html

1 Intuitive Limits and Continuity: When Limits Do Not Exist

diverges to negative infinity

Definition MYMACalc2 Limits - Definition,\MYMACalc2\Part IV - Sequences & Series\Seq\LimDef.html

2 Sequences: Limits - Definition

diverging

Definition MYMACalc3 Algebraic Definition of Divergence,\MYMACalc3\Part II - Derivatives\DivCurlPots\DivAlg.html

3 Divergence, Curl and Potentials: Algebraic Definition of Divergence

dividend

Definition MYMACalc2 General Decompositions,\MYMACalc2\Part I - Techniques of Integration\ParFrac\Decomp.html

2 Partial Fractions: General Decompositions

divisor

Definition MYMACalc2 General Decompositions,\MYMACalc2\Part I - Techniques of Integration\ParFrac\Decomp.html

2 Partial Fractions: General Decompositions

does not have a sum

Definition MYMACalc2 The Sum of a Series,\MYMACalc2\Part IV - Sequences & Series\Ser\Sum.html

2 Series: The Sum of a Series

dog saddle

Definition MYMACalc3 Functions of \(2\) Variables,\MYMACalc3\Part I - Geometry & Vectors\Functions\MaxMinSaddle2.html

3 Functions of Several Variables: Functions of \(2\) Variables

domain

Definition MYMACalc3 Domain and Image,\MYMACalc3\Part I - Geometry & Vectors\Functions\DomainImage.html

3 Functions of Several Variables: Domain and Image

dot product

Definition MYMACalc1 Dot Product - Algebraic,\MYMACalc1\Part I - Pre-Calculus\Vectors\DotAlg.html

1 Vectors: Dot Product - Algebraic

dot product

Definition MYMACalc3 Algebraic Definition,\MYMACalc3\Part I - Geometry & Vectors\Dot\DotAlg.html

3 Dot Product: Algebraic Definition

double integral of \(f(x,y)\) over the region \(R\)

Definition MYMACalc3 Riemann Sum Definition of Double Integrals,\MYMACalc3\Part III - Integrals\RiemInt\2DRiem.html

3 Multiple Integrals as Riemann Sums: Riemann Sum Definition of Double Integrals

drag coefficient

Definition MYMACalc2 Falling with Air Resistance,\MYMACalc2\Part III - Differential Equations\DEApps\TermVel.html

2 Applications of Differential Equations: Falling with Air Resistance

electric charge

Definition MYMACalc2 Electric Charge - Bar with Non-Uniform Charge Density,\MYMACalc2\Part II - Applications of Integration\Mass\Charge.html

2 Mass and Center of Mass: Electric Charge - Bar with Non-Uniform Charge Density

electrostatic potential energy

Definition MYMACalc3 Coulomb Electrostatic Force,\MYMACalc3\Part IV - Theorems\ThmFTCC\CoulombElectro.html

3 Fundamental Theorem of Calculus for Curves: Coulomb Electrostatic Force

Eliminate a Variable Method

Definition MYMACalc3 Eliminate a Variable Method,\MYMACalc3\Part II - Derivatives\MaxMin\Constraint.html,Multiple Constraint Problems (Optional),\MYMACalc3\Part II - Derivatives\MaxMin\MultConstraint.html

3 Max-Min Problems: Eliminate a Variable Method

ellipse

Definition MYMACalc3 Quadratic Curves - Part 1,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\CrvR2Quad1.html

3 Curves and Surfaces: Quadratic Curves - Part 1

ellipsoid

Definition MYMACalc3 Quadratic Surfaces - Part 1,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3Quad1.html

3 Curves and Surfaces: Quadratic Surfaces - Part 1

elliptic cylinders

Definition MYMACalc3 Quadratic Surfaces - Part 2,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3Quad2.html

3 Curves and Surfaces: Quadratic Surfaces - Part 2

elliptic polar coordinate system

Definition MYMACalc3 2D Curvilinear Coordinates - Ellipse Example,\MYMACalc3\Part III - Integrals\CurvInt\2DCurv-Int.html

3 Multiple Integrals in Curvilinear Coordinates: 2D Curvilinear Coordinates - Ellipse Example

elliptic paraboloid

Definition MYMACalc3 Quadratic Surfaces - Part 2,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3Quad2.html

3 Curves and Surfaces: Quadratic Surfaces - Part 2

equal to

Definition MYMACalc1 Precise Limits at Infinity,\MYMACalc1\Part II - Limits and Continuity\Precise\LimatInf.html,Precise Left and Right Limits,\MYMACalc1\Part II - Limits and Continuity\Precise\LRLims.html,Precise \(2\)-Sided Limits,\MYMACalc1\Part II - Limits and Continuity\Precise\Lims.html

1 Precise Limits and Continuity: Precise Limits at Infinity

equal to

Definition MYMACalc3 Precise Limits for Functions of \(1\) Variable (Optional Review),\MYMACalc3\Part II - Derivatives\LimCont\Prec_1D.html,Precise Limits for Functions of \(2\) Variables (Optional),\MYMACalc3\Part II - Derivatives\LimCont\Prec_2D.html

3 Limits and Continuity: Precise Limits for Functions of \(1\) Variable (Optional Review)

equal to

Definition MYMACalc2 Precise Definiton of Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\PrecDef.html

2 Sequences: Precise Definiton of Limits

Equation of a Tangent Plane to a Graph

Theorem MYMACalc3 Comparison of Tangent Line and Tangent Plane Derivations,\MYMACalc3\Part II - Derivatives\ParDerTanPlane\TanLinePlane.html,Tangent Plane to the Graph of a Function - Algebraic,\MYMACalc3\Part II - Derivatives\ParDerTanPlane\TanPlaneAlg.html

3 Partial Derivatives and Tangent Planes: Comparison of Tangent Line and Tangent Plane Derivations

Equation of a Circle

Theorem MYMACalc3 Distance Formula in 2D,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DDistance.html

3 Coordinate Systems: Distance Formula in 2D

Equation of a Sphere

Theorem MYMACalc3 Distance Formula in 3D,\MYMACalc3\Part I - Geometry & Vectors\Coords\3DDistance.html

3 Coordinate Systems: Distance Formula in 3D

Equation of a Tangent Line to a Graph

Theorem MYMACalc1 Tangent Lines,\MYMACalc1\Part III - Derivatives\DefTanLine\TanLine.html

1 Definitions and Tangent Lines: Tangent Lines

Equation of a Tangent Line to a Graph

Theorem MYMACalc3 Tangent Line to the Graph of a Function,\MYMACalc3\Part II - Derivatives\ParDerTanPlane\TanLine.html,Comparison of Tangent Line and Tangent Plane Derivations,\MYMACalc3\Part II - Derivatives\ParDerTanPlane\TanLinePlane.html

3 Partial Derivatives and Tangent Planes: Tangent Line to the Graph of a Function

Equation of a Tangent HyperPlane to a Graph

Theorem MYMACalc3 More Variables,\MYMACalc3\Part II - Derivatives\ParDerTanPlane\MoreVars.html

3 Partial Derivatives and Tangent Planes: More Variables

Equation of a Sphere in \(\mathbb{R}^n\)

Theorem MYMACalc3 Distance Formula in Higher Dimensions (Optional),\MYMACalc3\Part I - Geometry & Vectors\Coords\nDDistance.html

3 Coordinate Systems: Distance Formula in Higher Dimensions (Optional)

Equivalent Form

Theorem MYMACalc1 Limit Laws,\MYMACalc1\Part II - Limits and Continuity\Precise\LimLaws.html

1 Precise Limits and Continuity: Limit Laws

error in the approximation

Definition MYMACalc2 Approximating the Series,\MYMACalc2\Part IV - Sequences & Series\SerPos\ApproxSerIntegBnd.html

2 Convergence of Positive Series: Approximating the Series

evaluation point

Definition MYMACalc3 Riemann Sum Definition of Single Integrals (Review),\MYMACalc3\Part III - Integrals\RiemInt\1DRiem.html,Riemann Sum Definition of Double Integrals,\MYMACalc3\Part III - Integrals\RiemInt\2DRiem.html,Riemann Sum Definition of Triple Integrals,\MYMACalc3\Part III - Integrals\RiemInt\3DRiem.html

3 Multiple Integrals as Riemann Sums: Riemann Sum Definition of Single Integrals (Review)

evaluation point

Definition MYMACalc2 Riemann Sums and Integrals (Optional),\MYMACalc2\Part I - Techniques of Integration\RiemSum\Def2.html

2 Riemann Sums: Riemann Sums and Integrals (Optional)

evaluation point

Definition MYMACalc1 Riemann Sums and Integrals,\MYMACalc1\Part V - Integrals\RiemSum\Def2.html

1 Riemann Sums: Riemann Sums and Integrals

exists

Definition MYMACalc2 Precise Definiton of Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\PrecDef.html

2 Sequences: Precise Definiton of Limits

exists

3 Limits and Continuity: Precise Limits for Functions of \(1\) Variable (Optional Review)

exists

1 Precise Limits and Continuity: Precise Limits at Infinity

expanded

Definition MYMACalc2 What is a Power Series?,\MYMACalc2\Part IV - Sequences & Series\PowSer\Def.html

2 Power Series: What is a Power Series?

expanding

Definition MYMACalc3 Algebraic Definition of Divergence,\MYMACalc3\Part II - Derivatives\DivCurlPots\DivAlg.html

3 Divergence, Curl and Potentials: Algebraic Definition of Divergence

expansion of the fluid

Definition MYMACalc3 Expansion and Contraction,\MYMACalc3\Part I - Geometry & Vectors\LineInt\Expansion.html

3 Line Integrals: Expansion and Contraction

expansion of the vector field

Definition MYMACalc3 Expansion and Contraction,\MYMACalc3\Part I - Geometry & Vectors\LineInt\Expansion.html

3 Line Integrals: Expansion and Contraction

expansion by minors

Definition MYMACalc3 Expansion by Minors on a Row or Column,\MYMACalc3\Part I - Geometry & Vectors\Cross\DetExpn.html

3 Cross Product: Expansion by Minors on a Row or Column

expected value

Definition MYMACalc3 Average Value,\MYMACalc3\Part I - Geometry & Vectors\LineInt\Ave.html

3 Line Integrals: Average Value

explicit function definition

Definition MYMACalc3 Implicit Functions,\MYMACalc3\Part II - Derivatives\Chain\ImplicitDiff1.html

3 Chain Rule: Implicit Functions

explicit form of the solution

Definition MYMACalc2 Separable Differential Equations --- Example 2,\MYMACalc2\Part III - Differential Equations\DEIVP\esep2.html

2 Differential Equations and Initial Value Problems: Separable Differential Equations --- Example 2

explicit function definition

Definition MYMACalc1 Implicit Functions,\MYMACalc1\Part III - Derivatives\Chain\ImplicitDiff.html

1 Chain Rule & Implicit Differentiation: Implicit Functions

Exponential Sequences

Theorem MYMACalc1 Limits of Special Functions,\MYMACalc1\Part II - Limits and Continuity\Compute\LimSpec.html,Limits of Non-Linear Functions,\MYMACalc1\Part II - Limits and Continuity\Precise\NonLinear.html

1 Computing Limits: Limits of Special Functions

1 Precise Limits and Continuity: Limits of Non-Linear Functions

Exponential Sequences

Theorem MYMACalc2 Special Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\LimSpec.html,Precise Special Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\PrecSpec.html

2 Sequences: Special Limits

Extended Mean Value Theorem

Definition MYMACalc2 Taylor Remainder,\MYMACalc2\Part IV - Sequences & Series\Taylor\Remainder.html

2 Taylor Series: Taylor Remainder

extrema

3 Functions of Several Variables: Functions of \(1\) Variable

3 Max-Min Problems: Functions of \(2\) Variables

extremal

Definition MYMACalc3 Constrained Max-Min Problems,\MYMACalc3\Part II - Derivatives\MaxMin\Constraint.html

3 Max-Min Problems: Constrained Max-Min Problems

extreme cases

Definition MYMACalc2 The Limit Comparison Test - Proof,\MYMACalc2\Part IV - Sequences & Series\SerPos\LimCompPf.html,The Limit Comparison Test,\MYMACalc2\Part IV - Sequences & Series\SerPos\LimCompTest.html,The Limit Comparison Test - Extreme Cases,\MYMACalc2\Part IV - Sequences & Series\SerPos\LimCompTest2.html,Overview,\MYMACalc2\Part IV - Sequences & Series\SerPos\Overview.html

2 Convergence of Positive Series: The Limit Comparison Test - Proof

extremize

Definition MYMACalc3 Constrained Max-Min Problems,\MYMACalc3\Part II - Derivatives\MaxMin\Constraint.html

3 Max-Min Problems: Constrained Max-Min Problems

finite

Definition MYMACalc2 Definition,\MYMACalc2\Part IV - Sequences & Series\Seq\Def.html

2 Sequences: Definition

Finite Geometric Series

Theorem MYMACalc2 Geometric Series - Finite,\MYMACalc2\Part IV - Sequences & Series\Ser\GeomFin.html

2 Series: Geometric Series - Finite

finite geometric series

Definition MYMACalc2 Geometric Series - Finite,\MYMACalc2\Part IV - Sequences & Series\Ser\GeomFin.html

2 Series: Geometric Series - Finite

finite

Definition MYMACalc1 Limits at Infinity,\MYMACalc1\Part II - Limits and Continuity\Compute\LimatInf.html

1 Computing Limits: Limits at Infinity

finite series

Definition MYMACalc2 Definition,\MYMACalc2\Part IV - Sequences & Series\Ser\Def.html

2 Series: Definition

first moment of the mass

Definition MYMACalc2 Center of Mass - Bar with Non-Uniform Density,\MYMACalc2\Part II - Applications of Integration\Mass\CMbar.html,Center of Mass - Discrete Masses,\MYMACalc2\Part II - Applications of Integration\Mass\CMdiscrete.html,Moment of Inertia - Bar with Non-Uniform Density,\MYMACalc2\Part II - Applications of Integration\Mass\MomInertia.html

2 Mass and Center of Mass: Center of Mass - Bar with Non-Uniform Density

First Derivative Test

Theorem MYMACalc3 Local Minima, Local Maxima and Inflection Points of Functions of \(1\) Variable,\MYMACalc3\Part II - Derivatives\MaxMin\MinMaxInfl.html

3 Max-Min Problems: Local Minima, Local Maxima and Inflection Points of Functions of \(1\) Variable

first moments of the mass

Definition MYMACalc3 Mass, Center of Mass and Centroid,\MYMACalc3\Part I - Geometry & Vectors\LineInt\MassCM.html

3 Line Integrals: Mass, Center of Mass and Centroid

first moments of arc length

Definition MYMACalc3 Mass, Center of Mass and Centroid,\MYMACalc3\Part I - Geometry & Vectors\LineInt\MassCM.html

3 Line Integrals: Mass, Center of Mass and Centroid

first term

Definition MYMACalc2 Geometric Series - Finite,\MYMACalc2\Part IV - Sequences & Series\Ser\GeomFin.html,Geometric Series - Infinite,\MYMACalc2\Part IV - Sequences & Series\Ser\GeomInf.html

2 Series: Geometric Series - Finite

First Derivative Test

Theorem MYMACalc1 \(2^\text{nd}\) Derivative Test,\MYMACalc1\Part IV - Applications of Derivatives\MaxMin\2ndDerivTest.html

1 Max/Min Problems: \(2^\text{nd}\) Derivative Test

flow diagram

Definition MYMACalc2 Separable Differential Equations --- Example 2,\MYMACalc2\Part III - Differential Equations\DEIVP\esep2.html

2 Differential Equations and Initial Value Problems: Separable Differential Equations --- Example 2

flow of the fluid

Definition MYMACalc3 Flow and Circulation,\MYMACalc3\Part I - Geometry & Vectors\LineInt\FlowCirc.html

3 Line Integrals: Flow and Circulation

flow of the vector field

Definition MYMACalc3 Flow and Circulation,\MYMACalc3\Part I - Geometry & Vectors\LineInt\FlowCirc.html

3 Line Integrals: Flow and Circulation

for Manipulating the Hand.

Theorem MYMACalc3 Right Hand Rule,\MYMACalc3\Part I - Geometry & Vectors\Cross\CrossRHR.html

3 Cross Product: Right Hand Rule

force

Definition MYMACalc3 Application: Balancing Forces,\MYMACalc3\Part I - Geometry & Vectors\Vectors\BalForces.html

3 Vectors: Application: Balancing Forces

force

Definition MYMACalc1 Balancing Forces,\MYMACalc1\Part I - Pre-Calculus\Vectors\BalForces.html

1 Vectors: Balancing Forces

free scalar

Definition MYMACalc3 Free vs. Located,\MYMACalc3\Part I - Geometry & Vectors\Vectors\FreeVsLocated.html

3 Vectors: Free vs. Located

free vector

Definition MYMACalc3 Free vs. Located,\MYMACalc3\Part I - Geometry & Vectors\Vectors\FreeVsLocated.html

3 Vectors: Free vs. Located

free fall

Definition MYMACalc2 Free Fall,\MYMACalc2\Part III - Differential Equations\DEApps\FreeFall.html

2 Applications of Differential Equations: Free Fall

Frenet Equations

Theorem MYMACalc3 Frenet Frames & Derivatives of TNB,\MYMACalc3\Part I - Geometry & Vectors\CurveProps\Frenet.html

3 Properties of Curves: Frenet Frames & Derivatives of TNB

front

Definition MYMACalc3 Vector Surface Integrals,\MYMACalc3\Part III - Integrals\SurfInt\VecSurfInt.html

3 Parametric Surfaces and Surface Integrals: Vector Surface Integrals

frustrum of a cone

Definition MYMACalc2 Area of a Surface of Revolution,\MYMACalc2\Part II - Applications of Integration\ArcSurf\SurfRev.html

2 Arc Length and Surface Area: Area of a Surface of Revolution

frustum of a cone

Definition MYMACalc2 Area of a Surface of Revolution,\MYMACalc2\Part II - Applications of Integration\ArcSurf\SurfRev.html

2 Arc Length and Surface Area: Area of a Surface of Revolution

Fubini's Theorem: Integral over a Polar Rectangle

Theorem MYMACalc3 Polar Coordinates - Integral over a Polar Rectangle,\MYMACalc3\Part III - Integrals\CurvInt\Polar-Int.html

3 Multiple Integrals in Curvilinear Coordinates: Polar Coordinates - Integral over a Polar Rectangle

Fubini's Theorem

Theorem MYMACalc3 Polar Coordinates - Integral over a Polar Rectangle - Derivation,\MYMACalc3\Part III - Integrals\CurvInt\Polar-IntDerive.html,Computing Iterated Integrals with Constant Limits,\MYMACalc3\Part III - Integrals\IteratedInt\CompConstLims.html,Double Integrals over a Rectangle,\MYMACalc3\Part III - Integrals\RiemInt\2DRect.html,Triple Integrals over a Rectangular Box,\MYMACalc3\Part III - Integrals\RiemInt\3DRect.html

3 Multiple Integrals in Curvilinear Coordinates: Polar Coordinates - Integral over a Polar Rectangle - Derivation

3 Iterated Integrals: Computing Iterated Integrals with Constant Limits

3 Multiple Integrals as Riemann Sums: Double Integrals over a Rectangle

function

Definition MYMACalc3 Formulas,\MYMACalc3\Part I - Geometry & Vectors\Functions\Formulas.html

3 Functions of Several Variables: Formulas

Fundamental Theorem of Calculus for Curves (FTCC)

Theorem MYMACalc3 undefined,\MYMACalc3\Part IV - Theorems\ThmFTCC\Verify.html,The Theorem,\MYMACalc3\Part IV - Theorems\ThmFTCC\Theorem.html

3 Fundamental Theorem of Calculus for Curves: undefined

Gauss' Theorem without Holes

Theorem MYMACalc3 The Theorem,\MYMACalc3\Part IV - Theorems\ThmGauss\Theorem.html

3 Gauss' Theorem: The Theorem

Gauss' Theorem

Theorem MYMACalc3 undefined,\MYMACalc3\Part IV - Theorems\ThmGauss\x.html,The Theorem for Regions with Holes,\MYMACalc3\Part IV - Theorems\ThmGauss\Hole.html

3 Gauss' Theorem: undefined

general antiderivative

Definition MYMACalc1 Non-Uniqueness of Antiderivatives,\MYMACalc1\Part V - Integrals\AntiDer\NonUniq.html

1 Antiderivatives: Non-Uniqueness of Antiderivatives

general

Definition MYMACalc2 Overview,\MYMACalc2\Part IV - Sequences & Series\SerPos\Overview.html

2 Convergence of Positive Series: Overview

general antiderivative

Definition MYMACalc2 Non-Uniqueness of Antiderivatives,\MYMACalc2\Part I - Techniques of Integration\AntiDer\NonUniq.html

2 Antiderivatives: Non-Uniqueness of Antiderivatives

general series

Definition MYMACalc2 Overview,\MYMACalc2\Part IV - Sequences & Series\SerGen\Overview.html

2 Convergence of General Series: Overview

Geometric Formula for Dot Product

Theorem MYMACalc1 Dot Product - Geometric,\MYMACalc1\Part I - Pre-Calculus\Vectors\DotGeom.html

1 Vectors: Dot Product - Geometric

Geometric Formula for Dot Product

Theorem MYMACalc3 Geometric Formula,\MYMACalc3\Part I - Geometry & Vectors\Dot\DotGeom.html

3 Dot Product: Geometric Formula

Geometric Description of the Cross Product

Theorem MYMACalc3 Geometric Interpretation of Cross Products,\MYMACalc3\Part I - Geometry & Vectors\Cross\CrossGeom.html

3 Cross Product: Geometric Interpretation of Cross Products

geometric series

Definition MYMACalc2 Geometric Series - Finite,\MYMACalc2\Part IV - Sequences & Series\Ser\GeomFin.html

2 Series: Geometric Series - Finite

Geometric Interpretation of the Triple Product

Theorem MYMACalc3 Geometric Interpretation of Triple Products,\MYMACalc3\Part I - Geometry & Vectors\Cross\TripleGeom.html

3 Cross Product: Geometric Interpretation of Triple Products

geometrical domains

Definition MYMACalc3 Introduction to Parametric Surfaces,\MYMACalc3\Part III - Integrals\SurfInt\PosPlots.html

3 Parametric Surfaces and Surface Integrals: Introduction to Parametric Surfaces

global maximum

3 Functions of Several Variables: Functions of \(1\) Variable

3 Max-Min Problems: Functions of \(2\) Variables

global minimum

3 Functions of Several Variables: Functions of \(1\) Variable

3 Max-Min Problems: Functions of \(2\) Variables

gradient

Definition MYMACalc3 undefined,\MYMACalc3\Part II - Derivatives\DivCurlPots\DelOperator.html,The Del Operator,\MYMACalc3\Part II - Derivatives\DivCurlPots\DelOperator.html,The Hessian,\MYMACalc3\Part II - Derivatives\Higher\Hessian.html,Derivative Along a Curve and the Gradient,\MYMACalc3\Part II - Derivatives\DirDerivGrad\DerCurve.html

3 Divergence, Curl and Potentials: undefined

3 Higher Order Derivatives: The Del Operator

3 Directional Derivatives and Gradients: The Hessian

gradient field

Definition MYMACalc3 Non-Existence of a Scalar Potential,\MYMACalc3\Part II - Derivatives\DivCurlPots\NoScalPot.html

3 Divergence, Curl and Potentials: Non-Existence of a Scalar Potential

graph of the parametric curve

3 Curves and Surfaces: Curves in \(\mathbb{R}^2\)

graph of an equation in \(3\) variables

Definition MYMACalc3 Graphs of Equations,\MYMACalc3\Part I - Geometry & Vectors\Functions\Graphs2.html

3 Functions of Several Variables: Graphs of Equations

graph of a function of \(2\) variables

Definition MYMACalc3 Graphs of Functions,\MYMACalc3\Part I - Geometry & Vectors\Functions\Graphs.html

3 Functions of Several Variables: Graphs of Functions

graph of the parametric surface

Definition MYMACalc3 Surfaces in \(\mathbb{R}^3\),\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3.html

3 Curves and Surfaces: Surfaces in \(\mathbb{R}^3\)

graph of an equation in \(2\) variables

Definition MYMACalc3 Graphs of Equations,\MYMACalc3\Part I - Geometry & Vectors\Functions\Graphs2.html

3 Functions of Several Variables: Graphs of Equations

graph of the parametric curve

Definition MYMACalc1 Parametric Curves,\MYMACalc1\Part I - Pre-Calculus\Vectors\Curves.html

1 Vectors: Parametric Curves

graph of a function of \(3\) variables

Definition MYMACalc3 Graphs of Functions,\MYMACalc3\Part I - Geometry & Vectors\Functions\Graphs.html

3 Functions of Several Variables: Graphs of Functions

graph of a function of \(1\) variable

Definition MYMACalc3 Graphs of Functions,\MYMACalc3\Part I - Geometry & Vectors\Functions\Graphs.html

3 Functions of Several Variables: Graphs of Functions

gravitational potential energy

Definition MYMACalc3 Gravitational Force near the Earth,\MYMACalc3\Part IV - Theorems\ThmFTCC\EarthGrav.html,Newtonian Gravitational Force,\MYMACalc3\Part IV - Theorems\ThmFTCC\NewtonGrav.html

3 Fundamental Theorem of Calculus for Curves: Gravitational Force near the Earth

Green's Theorem

Theorem MYMACalc3 undefined,\MYMACalc3\Part IV - Theorems\ThmGreen\x.html,The Theorem for Regions with Holes,\MYMACalc3\Part IV - Theorems\ThmGreen\Hole.html

3 Green's Theorem: undefined

Green's Theorem without Holes

Theorem MYMACalc3 The Theorem,\MYMACalc3\Part IV - Theorems\ThmGreen\Theorem.html

3 Green's Theorem: The Theorem

grid cell

Definition MYMACalc3 2D Curvilinear Coordinates - Grid Cell Area,\MYMACalc3\Part III - Integrals\CurvInt\2DCurv-GridArea.html,Polar Coordinates - Grid Cell,\MYMACalc3\Part III - Integrals\CurvInt\Polar-Grid.html

3 Multiple Integrals in Curvilinear Coordinates: 2D Curvilinear Coordinates - Grid Cell Area

growth constant

Definition MYMACalc2 Separable Differential Equations --- Example 7,\MYMACalc2\Part III - Differential Equations\DEIVP\esep7.html

2 Differential Equations and Initial Value Problems: Separable Differential Equations --- Example 7

harmonic series

Definition MYMACalc2 The Integral Test,\MYMACalc2\Part IV - Sequences & Series\SerPos\IntegTest.html,The \(p\)-Series,\MYMACalc2\Part IV - Sequences & Series\SerPos\pSerTest.html

2 Convergence of Positive Series: The Integral Test

harmonic function

Definition MYMACalc3 The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian,\MYMACalc3\Part II - Derivatives\DivCurlPots\OpDivGrad.html

3 Divergence, Curl and Potentials: The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian

has sum \(S\)

Definition MYMACalc2 The Sum of a Series,\MYMACalc2\Part IV - Sequences & Series\Ser\Sum.html

2 Series: The Sum of a Series

has a limit

Definition MYMACalc2 Limits - Definition,\MYMACalc2\Part IV - Sequences & Series\Seq\LimDef.html

2 Sequences: Limits - Definition

\(\hat\imath\,\hat\jmath\,\hat k\) notation

Definition MYMACalc3 \(ijk\) Notation,\MYMACalc3\Part I - Geometry & Vectors\Vectors\ijkNote.html

3 Vectors: \(ijk\) Notation

\(\hat\imath\,\hat\jmath\,\hat k\) notation

Definition MYMACalc1 \(\hat\imath\hat\jmath\) Notation,\MYMACalc1\Part I - Pre-Calculus\Vectors\ijNote.html

1 Vectors: \(\hat\imath\hat\jmath\) Notation

Heat Equation

Definition MYMACalc3 The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian,\MYMACalc3\Part II - Derivatives\DivCurlPots\OpDivGrad.html

3 Divergence, Curl and Potentials: The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian

helicity

Definition MYMACalc3 Torsion,\MYMACalc3\Part I - Geometry & Vectors\CurveProps\Torsion.html

3 Properties of Curves: Torsion

helix

Definition MYMACalc2 Parametric Curves,\MYMACalc2\Part II - Applications of Integration\ArcSurf\ParamCrv.html

2 Arc Length and Surface Area: Parametric Curves

Hessian

Definition MYMACalc3 The Hessian,\MYMACalc3\Part II - Derivatives\Higher\Hessian.html

3 Higher Order Derivatives: The Hessian

horizontal axis

Definition MYMACalc3 2D Rectangular Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DRectCoord.html

3 Coordinate Systems: 2D Rectangular Coordinates

Horizontal and Vertical Tangents to a Parametric Curve

Theorem MYMACalc2 Horizontal and Vertical Tangents,\MYMACalc2\Part II - Applications of Integration\ArcSurf\ParamHVTan.html

2 Arc Length and Surface Area: Horizontal and Vertical Tangents

horizontal inflection points

Definition MYMACalc3 Functions of \(1\) Variable,\MYMACalc3\Part I - Geometry & Vectors\Functions\MaxMinSaddle.html

3 Functions of Several Variables: Functions of \(1\) Variable

horizontal inflection point

Definition MYMACalc1 \(2^\text{nd}\) Derivative Test,\MYMACalc1\Part IV - Applications of Derivatives\MaxMin\2ndDerivTest.html

1 Max/Min Problems: \(2^\text{nd}\) Derivative Test

horizontal inflection point

Definition MYMACalc3 Local Minima, Local Maxima and Inflection Points of Functions of \(1\) Variable,\MYMACalc3\Part II - Derivatives\MaxMin\MinMaxInfl.html

3 Max-Min Problems: Local Minima, Local Maxima and Inflection Points of Functions of \(1\) Variable

hyperbola

Definition MYMACalc3 Quadratic Curves - Part 1,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\CrvR2Quad1.html

3 Curves and Surfaces: Quadratic Curves - Part 1

hyperbolic paraboloid

Definition MYMACalc3 Quadratic Surfaces - Part 2,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3Quad2.html

3 Curves and Surfaces: Quadratic Surfaces - Part 2

hyperbolic cylinders

Definition MYMACalc3 Quadratic Surfaces - Part 2,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3Quad2.html

3 Curves and Surfaces: Quadratic Surfaces - Part 2

hyperboloid of one sheet

Definition MYMACalc3 Quadratic Surfaces - Part 1,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3Quad1.html

3 Curves and Surfaces: Quadratic Surfaces - Part 1

hyperboloid of two sheets

Definition MYMACalc3 Quadratic Surfaces - Part 1,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3Quad1.html

3 Curves and Surfaces: Quadratic Surfaces - Part 1

Identity Sequence

Theorem MYMACalc1 Limits of Special Functions,\MYMACalc1\Part II - Limits and Continuity\Compute\LimSpec.html,Limit Laws,\MYMACalc1\Part II - Limits and Continuity\Precise\LimLaws.html

1 Computing Limits: Limits of Special Functions

1 Precise Limits and Continuity: Limit Laws

Identity Sequence

Theorem MYMACalc2 Special Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\LimSpec.html,Precise Special Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\PrecSpec.html

2 Sequences: Special Limits

\(ij\)-entry in the Hessian

Definition MYMACalc3 The Hessian,\MYMACalc3\Part II - Derivatives\Higher\Hessian.html

3 Higher Order Derivatives: The Hessian

image

Definition MYMACalc3 Domain and Image,\MYMACalc3\Part I - Geometry & Vectors\Functions\DomainImage.html

3 Functions of Several Variables: Domain and Image

implicit function definition

Definition MYMACalc1 Implicit Functions,\MYMACalc1\Part III - Derivatives\Chain\ImplicitDiff.html

1 Chain Rule & Implicit Differentiation: Implicit Functions

implicit function definition

Definition MYMACalc3 Implicit Functions,\MYMACalc3\Part II - Derivatives\Chain\ImplicitDiff1.html

3 Chain Rule: Implicit Functions

implicit form of the solution

Definition MYMACalc2 Separable Differential Equations --- Example 2,\MYMACalc2\Part III - Differential Equations\DEIVP\esep2.html

2 Differential Equations and Initial Value Problems: Separable Differential Equations --- Example 2

Improper Integrals of Inverse Powers

Theorem MYMACalc2 Relation between \(\displaystyle\int\dfrac{1}{x^p}\,dx\) and \(\displaystyle\int\dfrac{1}{\sqrt[p]{x}}\,dx\),\MYMACalc2\Part I - Techniques of Integration\Improper\InverseN.html

2 Improper Integrals: Relation between \(\displaystyle\int\dfrac{1}{x^p}\,dx\) and \(\displaystyle\int\dfrac{1}{\sqrt[p]{x}}\,dx\)

Improved Comparison Bound on the Error in an Approximation

Theorem MYMACalc2 Improving the Approximation Using Comparisons,\MYMACalc2\Part IV - Sequences & Series\SerPos\ApproxSerCompBnd2.html

2 Convergence of Positive Series: Improving the Approximation Using Comparisons

Improved Integral Bound on the Error in an Approximation

Theorem MYMACalc2 Improving the Approximation Using Integrals,\MYMACalc2\Part IV - Sequences & Series\SerPos\ApproxSerIntegBnd2.html

2 Convergence of Positive Series: Improving the Approximation Using Integrals

Improved Alternating Series Bound on the Error in an Approximation

Theorem MYMACalc2 Improving the Approximation for an Alternating Series,\MYMACalc2\Part IV - Sequences & Series\SerGen\ApproxSerAltBnd2.html

2 Convergence of General Series: Improving the Approximation for an Alternating Series

In summary:

Theorem MYMACalc3 2D Curvilinear Coordinates - The Jacobian,\MYMACalc3\Part III - Integrals\CurvInt\2DCurv-Jac.html

3 Multiple Integrals in Curvilinear Coordinates: 2D Curvilinear Coordinates - The Jacobian

incompressible

3 Divergence, Curl and Potentials: Algebraic Definition of Divergence

increasing

Definition MYMACalc2 Monotonic Sequences,\MYMACalc2\Part IV - Sequences & Series\Seq\Mono.html

2 Sequences: Monotonic Sequences

indefinite integral

Definition MYMACalc2 Indefinite Integrals,\MYMACalc2\Part I - Techniques of Integration\RiemSum\IndefInt.html

2 Riemann Sums: Indefinite Integrals

independent

Definition MYMACalc3 Chain Rule with \(1\) Intermediate Variable,\MYMACalc3\Part II - Derivatives\Chain\ChainRule1.html

3 Chain Rule: Chain Rule with \(1\) Intermediate Variable

independent

Definition MYMACalc1 Chain Rule,\MYMACalc1\Part III - Derivatives\Chain\Chain.html

1 Chain Rule & Implicit Differentiation: Chain Rule

independent variable

Definition MYMACalc2 What is a Differential Equation?,\MYMACalc2\Part III - Differential Equations\DEIVP\Def.html

2 Differential Equations and Initial Value Problems: What is a Differential Equation?

independent variables

Definition MYMACalc3 Formulas,\MYMACalc3\Part I - Geometry & Vectors\Functions\Formulas.html

3 Functions of Several Variables: Formulas

indeterminate forms

Definition MYMACalc1 Limit Laws,\MYMACalc1\Part II - Limits and Continuity\Compute\LimLaws.html

1 Computing Limits: Limit Laws

indeterminate forms

Definition MYMACalc2 Limit Laws,\MYMACalc2\Part IV - Sequences & Series\Seq\LimLaws.html,Limits Without Limit Laws,\MYMACalc2\Part IV - Sequences & Series\Seq\LimWOLaws.html

2 Sequences: Limit Laws

indirect

Definition MYMACalc3 Higher Derivatives,\MYMACalc3\Part II - Derivatives\Higher\HigherDer.html

3 Higher Order Derivatives: Higher Derivatives

infinite

Definition MYMACalc2 Definition,\MYMACalc2\Part IV - Sequences & Series\Seq\Def.html

2 Sequences: Definition

infinite series

Definition MYMACalc2 Definition,\MYMACalc2\Part IV - Sequences & Series\Ser\Def.html

2 Series: Definition

infinite

Definition MYMACalc1 Limits at Infinity,\MYMACalc1\Part II - Limits and Continuity\Compute\LimatInf.html

1 Computing Limits: Limits at Infinity

Infinite Limit of a Sequence

Definition MYMACalc2 Limits - Definition,\MYMACalc2\Part IV - Sequences & Series\Seq\LimDef.html

2 Sequences: Limits - Definition

infinite geometric series

Definition MYMACalc2 Geometric Series - Infinite,\MYMACalc2\Part IV - Sequences & Series\Ser\GeomInf.html

2 Series: Geometric Series - Infinite

Infinite Geometric Series

Theorem MYMACalc2 Geometric Series - Infinite,\MYMACalc2\Part IV - Sequences & Series\Ser\GeomInf.html

2 Series: Geometric Series - Infinite

Infinite Limit from the Right

Definition MYMACalc1 Precise Infinite Limits,\MYMACalc1\Part II - Limits and Continuity\Precise\InfLim.html

1 Precise Limits and Continuity: Precise Infinite Limits

initial value problem

Definition MYMACalc2 Differential Equations and Initial Value Problems,\MYMACalc2\Part I - Techniques of Integration\AntiDer\DiffEq.html

2 Antiderivatives: Differential Equations and Initial Value Problems

initial terms

Definition MYMACalc2 Recursively Defined Sequences,\MYMACalc2\Part IV - Sequences & Series\Seq\Recur.html

2 Sequences: Recursively Defined Sequences

initial value problem

Definition MYMACalc1 From Acceleration to Velocity and Position,\MYMACalc1\Part V - Integrals\AntiDer\AccVelPos.html

1 Antiderivatives: From Acceleration to Velocity and Position

inner product

Definition MYMACalc1 Dot Product - Algebraic,\MYMACalc1\Part I - Pre-Calculus\Vectors\DotAlg.html

1 Vectors: Dot Product - Algebraic

inner

Definition MYMACalc3 Chain Rule with \(1\) Intermediate Variable,\MYMACalc3\Part II - Derivatives\Chain\ChainRule1.html

3 Chain Rule: Chain Rule with \(1\) Intermediate Variable

inner

Definition MYMACalc1 Chain Rule,\MYMACalc1\Part III - Derivatives\Chain\Chain.html

1 Chain Rule & Implicit Differentiation: Chain Rule

inner product

Definition MYMACalc3 Algebraic Definition,\MYMACalc3\Part I - Geometry & Vectors\Dot\DotAlg.html

3 Dot Product: Algebraic Definition

input tolerance

3 Limits and Continuity: Precise Limits for Functions of \(1\) Variable (Optional Review)

input tolerance

Definition MYMACalc1 Precise Infinite Limits,\MYMACalc1\Part II - Limits and Continuity\Precise\InfLim.html,Precise Left and Right Limits,\MYMACalc1\Part II - Limits and Continuity\Precise\LRLims.html

1 Precise Limits and Continuity: Precise Infinite Limits

integral converges

Definition MYMACalc2 Integrals Improper at a Finite Endpoint,\MYMACalc2\Part I - Techniques of Integration\Improper\Fin.html,Integrals Improper at an Infinite Endpoint,\MYMACalc2\Part I - Techniques of Integration\Improper\Inf.html

2 Improper Integrals: Integrals Improper at a Finite Endpoint

integral of \(f(x)\) from \(x=a\) to \(x=b\)

Definition MYMACalc3 Riemann Sum Definition of Single Integrals (Review),\MYMACalc3\Part III - Integrals\RiemInt\1DRiem.html

3 Multiple Integrals as Riemann Sums: Riemann Sum Definition of Single Integrals (Review)

integral

Definition MYMACalc1 Riemann Sums and Areas,\MYMACalc1\Part V - Integrals\RiemSum\Def.html

1 Riemann Sums: Riemann Sums and Areas

Integral over a Type \(x\) Region

Theorem MYMACalc3 Double Integrals over a Non-Rectangular Region - Derivations,\MYMACalc3\Part III - Integrals\RectInt\2D-NonRectDerive.html

3 Multiple Integrals in Rectangular Coordinates: Double Integrals over a Non-Rectangular Region - Derivations

integral function for \(f(x)\)

Definition MYMACalc1 The Fundamental Theorem of Calculus for Integrals,\MYMACalc1\Part V - Integrals\RiemSum\IntFTC.html

1 Riemann Sums: The Fundamental Theorem of Calculus for Integrals

Integral over a Type \(r\) Region

Theorem MYMACalc3 Polar Coordinates - Integral over a Non-Rectangular Region,\MYMACalc3\Part III - Integrals\CurvInt\Polar-Int2.html,Polar Coordinates - Integral over a Non-Rectangular Region - Derivations,\MYMACalc3\Part III - Integrals\CurvInt\Polar-Int2Derive.html

3 Multiple Integrals in Curvilinear Coordinates: Polar Coordinates - Integral over a Non-Rectangular Region

integral function for \(f(x)\)

Definition MYMACalc2 The Fundamental Theorem of Calculus for Integrals,\MYMACalc2\Part I - Techniques of Integration\RiemSum\IntFTC.html

2 Riemann Sums: The Fundamental Theorem of Calculus for Integrals

Integral over a Type \(\theta\) Region

3 Multiple Integrals in Curvilinear Coordinates: Polar Coordinates - Integral over a Non-Rectangular Region

Integral over a Type \(y\) Region

Theorem MYMACalc3 Double Integrals over a Non-Rectangular Region - Derivations,\MYMACalc3\Part III - Integrals\RectInt\2D-NonRectDerive.html

3 Multiple Integrals in Rectangular Coordinates: Double Integrals over a Non-Rectangular Region - Derivations

integral bound on the error in the approximation

Definition MYMACalc2 Approximating the Series - Integral Bounds,\MYMACalc2\Part IV - Sequences & Series\SerPos\ApproxSerIntegBnd.html

2 Convergence of Positive Series: Approximating the Series - Integral Bounds

integral diverges

2 Improper Integrals: Integrals Improper at a Finite Endpoint

integrate a differential equation

Definition MYMACalc2 Solutions of Differential Equations,\MYMACalc2\Part III - Differential Equations\DEIVP\Sol.html

2 Differential Equations and Initial Value Problems: Solutions of Differential Equations

Integration by Parts

Theorem MYMACalc2 Definite Integrals,\MYMACalc2\Part I - Techniques of Integration\IntParts\Def.html,Indefinite Integrals,\MYMACalc2\Part I - Techniques of Integration\IntParts\Indef.html

2 Integration by Parts: Definite Integrals

Integration by Substitution

Theorem MYMACalc2 Indefinite Integrals,\MYMACalc2\Part I - Techniques of Integration\IntSubs\Indef.html

2 Integration by Substitution: Indefinite Integrals

Integration by Substitution

Theorem MYMACalc1 Indefinite Integrals,\MYMACalc1\Part V - Integrals\IntSubs\Indef.html

1 Integration by Substitution: Indefinite Integrals

Integrations of Power Series

Theorem MYMACalc2 Integration,\MYMACalc2\Part IV - Sequences & Series\PowSer\Integ.html

2 Power Series: Integration

intermediate

Definition MYMACalc1 Chain Rule,\MYMACalc1\Part III - Derivatives\Chain\Chain.html

1 Chain Rule & Implicit Differentiation: Chain Rule

intermediate

Definition MYMACalc3 Chain Rule with \(1\) Intermediate Variable,\MYMACalc3\Part II - Derivatives\Chain\ChainRule1.html

3 Chain Rule: Chain Rule with \(1\) Intermediate Variable

Interpretation of an Integral as Net Area

Theorem MYMACalc2 Riemann Sums and Integrals (Optional),\MYMACalc2\Part I - Techniques of Integration\RiemSum\Def2.html

2 Riemann Sums: Riemann Sums and Integrals (Optional)

Interpretation of Integral as Net Area

Theorem MYMACalc1 Riemann Sums and Integrals,\MYMACalc1\Part V - Integrals\RiemSum\Def2.html

1 Riemann Sums: Riemann Sums and Integrals

interval of convergence

Definition MYMACalc2 Sequences and Series of Functions,\MYMACalc2\Part IV - Sequences & Series\PowSer\SeqSerFns.html

2 Power Series: Sequences and Series of Functions

interval of convergence

Definition MYMACalc2 Interval of Convergence,\MYMACalc2\Part IV - Sequences & Series\PowSer\Interval.html

2 Power Series: Interval of Convergence

inverse

Definition MYMACalc2 Complex Methods (Optional),\MYMACalc2\Part I - Techniques of Integration\ParFrac\Coeffs2Complex.html

2 Partial Fractions: Complex Methods (Optional)

irreducible

Definition MYMACalc2 General Decompositions,\MYMACalc2\Part I - Techniques of Integration\ParFrac\Decomp.html

2 Partial Fractions: General Decompositions

irrotational

3 Divergence, Curl and Potentials: Algebraic Definition of Curl

is convergent

Definition MYMACalc2 The Sum of a Series,\MYMACalc2\Part IV - Sequences & Series\Ser\Sum.html

2 Series: The Sum of a Series

iterated double integral

Definition MYMACalc3 Computing Iterated Integrals with Constant Limits,\MYMACalc3\Part III - Integrals\IteratedInt\CompConstLims.html

3 Iterated Integrals: Computing Iterated Integrals with Constant Limits

iterated integral

Definition MYMACalc3 Computing Iterated Integrals with Constant Limits,\MYMACalc3\Part III - Integrals\IteratedInt\CompConstLims.html

3 Iterated Integrals: Computing Iterated Integrals with Constant Limits

iterated triple integral

Definition MYMACalc3 Computing Iterated Integrals with Constant Limits,\MYMACalc3\Part III - Integrals\IteratedInt\CompConstLims.html

3 Iterated Integrals: Computing Iterated Integrals with Constant Limits

Jacobian determinant

Definition MYMACalc3 3D Curvilinear Coordinates - The Jacobian,\MYMACalc3\Part III - Integrals\CurvInt\3DCurv-Jac.html

3 Multiple Integrals in Curvilinear Coordinates: 3D Curvilinear Coordinates - The Jacobian

Jacobian factor

Definition MYMACalc3 2D Curvilinear Coordinates - Grid Cell Area,\MYMACalc3\Part III - Integrals\CurvInt\2DCurv-GridArea.html,3D Curvilinear Coordinates - Grid Cell Volume,\MYMACalc3\Part III - Integrals\CurvInt\3DCurv-GridVol.html

3 Multiple Integrals in Curvilinear Coordinates: 2D Curvilinear Coordinates - Grid Cell Area

Jacobian Factor:

Definition MYMACalc3 2D Curvilinear Coordinates - The Jacobian,\MYMACalc3\Part III - Integrals\CurvInt\2DCurv-Jac.html

3 Multiple Integrals in Curvilinear Coordinates: 2D Curvilinear Coordinates - The Jacobian

Jacobian Matrix:

Definition MYMACalc3 2D Curvilinear Coordinates - The Jacobian,\MYMACalc3\Part III - Integrals\CurvInt\2DCurv-Jac.html

3 Multiple Integrals in Curvilinear Coordinates: 2D Curvilinear Coordinates - The Jacobian

Jacobian Determinant:

Definition MYMACalc3 2D Curvilinear Coordinates - The Jacobian,\MYMACalc3\Part III - Integrals\CurvInt\2DCurv-Jac.html

3 Multiple Integrals in Curvilinear Coordinates: 2D Curvilinear Coordinates - The Jacobian

\(k^\text{th}\) moment of the mass

2 Mass and Center of Mass: Center of Mass - Bar with Non-Uniform Density

\(k^\text{th}\) partial sum

Definition MYMACalc2 The Sum of a Series,\MYMACalc2\Part IV - Sequences & Series\Ser\Sum.html

2 Series: The Sum of a Series

\(k^\text{th}\) degree Taylor polynomial

Definition MYMACalc3 Taylor Series and Polynomials for \(2\) Variable,\MYMACalc3\Part II - Derivatives\Higher\Taylor2.html,Taylor Series and Polynomials for \(1\) Variable (Review),\MYMACalc3\Part II - Derivatives\Higher\Taylor.html

3 Higher Order Derivatives: Taylor Series and Polynomials for \(2\) Variable

Lagrange equations

Definition MYMACalc3 Lagrange Multiplier Method,\MYMACalc3\Part II - Derivatives\MaxMin\Lagrange.html

3 Max-Min Problems: Lagrange Multiplier Method

Lagrange Multiplier Method

Theorem MYMACalc3 Multiple Constraint Problems (Optional),\MYMACalc3\Part II - Derivatives\MaxMin\MultConstraint.html

3 Max-Min Problems: Multiple Constraint Problems (Optional)

Lagrange multiplier

Definition MYMACalc3 Lagrange Multiplier Method,\MYMACalc3\Part II - Derivatives\MaxMin\Lagrange.html

3 Max-Min Problems: Lagrange Multiplier Method

Laplace Equation

Definition MYMACalc3 The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian,\MYMACalc3\Part II - Derivatives\DivCurlPots\OpDivGrad.html

3 Divergence, Curl and Potentials: The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian

Laplacian

Definition MYMACalc3 The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian,\MYMACalc3\Part II - Derivatives\DivCurlPots\OpDivGrad.html

3 Divergence, Curl and Potentials: The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian

Law of Cosines

Theorem MYMACalc3 Geometric Formula,\MYMACalc3\Part I - Geometry & Vectors\Dot\DotGeom.html

3 Dot Product: Geometric Formula

Law of Cosines

Theorem MYMACalc1 Dot Product - Geometric,\MYMACalc1\Part I - Pre-Calculus\Vectors\DotGeom.html

1 Vectors: Dot Product - Geometric

leading principle minor determinants

Definition MYMACalc3 Second Derivative Test with More Variables (Optional),\MYMACalc3\Part II - Derivatives\MaxMin\SecondDerTest2.html

3 Max-Min Problems: Second Derivative Test with More Variables (Optional)

Left Riemann Sum Error and Bound Theorem

Theorem MYMACalc2 Error Bounds - Left and Right Riemann Sums,\MYMACalc2\Part I - Techniques of Integration\NumInt\LRErr.html

2 Numerical Integration: Error Bounds - Left and Right Riemann Sums

left handed system

Definition MYMACalc3 Geometric Interpretation of Triple Products,\MYMACalc3\Part I - Geometry & Vectors\Cross\TripleGeom.html

3 Cross Product: Geometric Interpretation of Triple Products

left or right limit is positive infinity

Definition MYMACalc1 When Limits Do Not Exist,\MYMACalc1\Part II - Limits and Continuity\Intuitive\LRLims.html

1 Intuitive Limits and Continuity: When Limits Do Not Exist

left or right limit is negative infinity

Definition MYMACalc3 When Limits Do Not Exist,\MYMACalc3\Part II - Derivatives\LimCont\Lim_1D.html

3 Limits and Continuity: When Limits Do Not Exist

left or right limit is negative infinity

Definition MYMACalc1 When Limits Do Not Exist,\MYMACalc1\Part II - Limits and Continuity\Intuitive\LRLims.html

1 Intuitive Limits and Continuity: When Limits Do Not Exist

left or right limit is positive infinity

Definition MYMACalc3 When Limits Do Not Exist,\MYMACalc3\Part II - Derivatives\LimCont\Lim_1D.html

3 Limits and Continuity: When Limits Do Not Exist

left or right limit is oscillitory divergent

Definition MYMACalc1 When Limits Do Not Exist,\MYMACalc1\Part II - Limits and Continuity\Intuitive\LRLims.html

1 Intuitive Limits and Continuity: When Limits Do Not Exist

left or right limit is oscillitory divergent

Definition MYMACalc3 When Limits Do Not Exist,\MYMACalc3\Part II - Derivatives\LimCont\Lim_1D.html

3 Limits and Continuity: When Limits Do Not Exist

length

Definition MYMACalc1 Magnitude,\MYMACalc1\Part I - Pre-Calculus\Vectors\Mag.html

1 Vectors: Magnitude

length

Definition MYMACalc2 Complex Methods (Optional),\MYMACalc2\Part I - Techniques of Integration\ParFrac\Coeffs2Complex.html

2 Partial Fractions: Complex Methods (Optional)

length

Definition MYMACalc3 Magnitude,\MYMACalc3\Part I - Geometry & Vectors\Vectors\Mag.html

3 Vectors: Magnitude

level set

Definition MYMACalc3 Level Sets and Contour Plots,\MYMACalc3\Part I - Geometry & Vectors\Functions\ContPlot3.html

3 Functions of Several Variables: Level Sets and Contour Plots

level surfaces

Definition MYMACalc3 Functions of \(3\) Variables,\MYMACalc3\Part I - Geometry & Vectors\Functions\ContPlot3.html

3 Functions of Several Variables: Functions of \(3\) Variables

level curves

Definition MYMACalc3 Functions of \(2\) Variables,\MYMACalc3\Part I - Geometry & Vectors\Functions\ContPlot2.html

3 Functions of Several Variables: Functions of \(2\) Variables

level point

Definition MYMACalc3 Functions of \(1\) Variable,\MYMACalc3\Part I - Geometry & Vectors\Functions\ContPlot.html

3 Functions of Several Variables: Functions of \(1\) Variable

limit of the function, \(f(x)\), as \(x\) approaches \(a\) from the left is infinity

Definition MYMACalc1 Precise Infinite Limits,\MYMACalc1\Part II - Limits and Continuity\Precise\InfLim.html

1 Precise Limits and Continuity: Precise Infinite Limits

limit of the function, \(f(x)\), as \(x\) approaches \(a\) from the right

Definition MYMACalc3 Intuitive Limits for Functions of 1 Variable (Review),\MYMACalc3\Part II - Derivatives\LimCont\Lim_1D.html

3 Limits and Continuity: Intuitive Limits for Functions of 1 Variable (Review)

limit of the function, \(f(x)\), as \(x\) approaches \(a\) from the right

Definition MYMACalc1 Left and Right Limits,\MYMACalc1\Part II - Limits and Continuity\Intuitive\LRLims.html

1 Intuitive Limits and Continuity: Left and Right Limits

limit of the function, \(f(x)\), as \(x\) approaches \(a\) from the left

Definition MYMACalc1 Left and Right Limits,\MYMACalc1\Part II - Limits and Continuity\Intuitive\LRLims.html

1 Intuitive Limits and Continuity: Left and Right Limits

limit of the function, \(f(x)\), as \(x\) approaches \(a\) from the left

Definition MYMACalc3 Intuitive Limits for Functions of 1 Variable (Review),\MYMACalc3\Part II - Derivatives\LimCont\Lim_1D.html

3 Limits and Continuity: Intuitive Limits for Functions of 1 Variable (Review)

limit of the \(n^\text{th}\) root of the \(n^\text{th}\) term

Definition MYMACalc2 Overview,\MYMACalc2\Part IV - Sequences & Series\SerPos\Overview.html,The Root Test - Proof,\MYMACalc2\Part IV - Sequences & Series\SerPos\RootPf.html,The Root Test,\MYMACalc2\Part IV - Sequences & Series\SerPos\RootTest.html

2 Convergence of Positive Series: Overview

limit of the ratio of successive terms

Definition MYMACalc2 Overview,\MYMACalc2\Part IV - Sequences & Series\SerPos\Overview.html,The Ratio Test - Proof,\MYMACalc2\Part IV - Sequences & Series\SerPos\RatioPf.html,The Ratio Test,\MYMACalc2\Part IV - Sequences & Series\SerPos\RatioTest.html

2 Convergence of Positive Series: Overview

limit of a vector function

Definition MYMACalc3 Limits of Vector Functions,\MYMACalc3\Part I - Geometry & Vectors\CurveProps\Lim.html

3 Properties of Curves: Limits of Vector Functions

Limit Laws

Theorem MYMACalc3 Limit Laws,\MYMACalc3\Part II - Derivatives\LimCont\LimLaws.html

3 Limits and Continuity: Limit Laws

limit

Definition MYMACalc2 Precise Definiton of Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\PrecDef.html

2 Sequences: Precise Definiton of Limits

Limit Laws

Theorem MYMACalc1 Limit Laws,\MYMACalc1\Part II - Limits and Continuity\Precise\LimLaws.html

1 Computing Limits: Limit Laws

1 Precise Limits and Continuity:

Limit of a Function from the Right

Definition MYMACalc1 Precise Left and Right Limits,\MYMACalc1\Part II - Limits and Continuity\Precise\LRLims.html

1 Precise Limits and Continuity: Precise Left and Right Limits

limit

Definition MYMACalc3 Intuitive Limits for Functions of 1 Variable (Review),\MYMACalc3\Part II - Derivatives\LimCont\Lim_1D.html,Precise Limits for Functions of \(1\) Variable (Optional Review),\MYMACalc3\Part II - Derivatives\LimCont\Prec_1D.html,Precise Limits for Functions of \(2\) Variables (Optional),\MYMACalc3\Part II - Derivatives\LimCont\Prec_2D.html

3 Limits and Continuity: Intuitive Limits for Functions of 1 Variable (Review)

limit of the function, \(f(x)\), as \(x\) approaches \(a\) from the right

Definition MYMACalc1 Precise Left and Right Limits,\MYMACalc1\Part II - Limits and Continuity\Precise\LRLims.html

1 Precise Limits and Continuity: Precise Left and Right Limits

limit of the absolute value of the ratio of successive terms

Definition MYMACalc2 Overview,\MYMACalc2\Part IV - Sequences & Series\SerGen\Overview.html,The Ratio Test,\MYMACalc2\Part IV - Sequences & Series\SerGen\Ratio.html,The Ratio Test - Proof,\MYMACalc2\Part IV - Sequences & Series\SerGen\RatioPf.html

2 Convergence of General Series: Overview

limit

Definition MYMACalc1 2-Sided Limits and Continuity,\MYMACalc1\Part II - Limits and Continuity\Intuitive\LimCont.html,Precise Limits at Infinity,\MYMACalc1\Part II - Limits and Continuity\Precise\LimatInf.html,Precise Left and Right Limits,\MYMACalc1\Part II - Limits and Continuity\Precise\LRLims.html,Precise \(2\)-Sided Limits,\MYMACalc1\Part II - Limits and Continuity\Precise\Lims.html

1 Intuitive Limits and Continuity: 2-Sided Limits and Continuity

1 Precise Limits and Continuity: Precise Limits at Infinity

limit from the right

Definition MYMACalc2 Integrals Improper at a Finite Endpoint,\MYMACalc2\Part I - Techniques of Integration\Improper\Fin.html

2 Improper Integrals: Integrals Improper at a Finite Endpoint

Limit of a Sequence

Definition MYMACalc2 Limits - Definition,\MYMACalc2\Part IV - Sequences & Series\Seq\LimDef.html,Precise Definiton of Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\PrecDef.html

2 Sequences: Limits - Definition

limit of the function, \(f(x)\), as \(x\) approaches \(a\) from the right is infinity

Definition MYMACalc1 Precise Infinite Limits,\MYMACalc1\Part II - Limits and Continuity\Precise\InfLim.html

1 Precise Limits and Continuity: Precise Infinite Limits

limit of the function, \(f(x)\), as \(x\) approaches \(a\) from the right is negative infinity

Definition MYMACalc1 Precise Infinite Limits,\MYMACalc1\Part II - Limits and Continuity\Precise\InfLim.html

1 Precise Limits and Continuity: Precise Infinite Limits

limit of the \(n^\text{th}\) root of the absolute value of the \(n^\text{th}\) term

Definition MYMACalc2 Overview,\MYMACalc2\Part IV - Sequences & Series\SerGen\Overview.html,The Root Test,\MYMACalc2\Part IV - Sequences & Series\SerGen\Root.html,The Root Test - Proof,\MYMACalc2\Part IV - Sequences & Series\SerGen\RootPf.html

2 Convergence of General Series: Overview

limit of the function, \(f(x)\), as \(x\) approaches \(a\) from the left is negative infinity

Definition MYMACalc1 Precise Infinite Limits,\MYMACalc1\Part II - Limits and Continuity\Precise\InfLim.html

1 Precise Limits and Continuity: Precise Infinite Limits

Limit Laws

Theorem MYMACalc2 Limit Laws,\MYMACalc2\Part IV - Sequences & Series\Seq\LimLaws.html,Precise Limit Laws,\MYMACalc2\Part IV - Sequences & Series\Seq\PrecLaws.html

2 Sequences: Limit Laws

Limit of a Function from the Right

Definition MYMACalc3 Precise Limits for Functions of \(1\) Variable (Optional Review),\MYMACalc3\Part II - Derivatives\LimCont\Prec_1D.html

3 Limits and Continuity: Precise Limits for Functions of \(1\) Variable (Optional Review)

limit of the function, \(f(x)\), as \(x\) approaches \(a\) is infinity

Definition MYMACalc1 Precise Infinite Limits,\MYMACalc1\Part II - Limits and Continuity\Precise\InfLim.html

1 Precise Limits and Continuity: Precise Infinite Limits

limit of the function, \(f(x)\), as \(x\) approaches \(a\) from the right

Definition MYMACalc3 Precise Limits for Functions of \(1\) Variable (Optional Review),\MYMACalc3\Part II - Derivatives\LimCont\Prec_1D.html

3 Limits and Continuity: Precise Limits for Functions of \(1\) Variable (Optional Review)

limit of the function, \(f(x,y)\), as \((x,y)\) approaches \((a,b)\)

Definition MYMACalc3 Precise Limits for Functions of \(2\) Variables (Optional),\MYMACalc3\Part II - Derivatives\LimCont\Prec_2D.html

3 Limits and Continuity: Precise Limits for Functions of \(2\) Variables (Optional)

limit of the function, \(f(x)\), as \(x\) approaches \(a\) is negative infinity

Definition MYMACalc1 Precise Infinite Limits,\MYMACalc1\Part II - Limits and Continuity\Precise\InfLim.html

1 Precise Limits and Continuity: Precise Infinite Limits

Limit of a Function of \(2\) Variables

Definition MYMACalc3 Precise Limits for Functions of \(2\) Variables (Optional),\MYMACalc3\Part II - Derivatives\LimCont\Prec_2D.html

3 Limits and Continuity: Precise Limits for Functions of \(2\) Variables (Optional)

limit of a difference quotient

Definition MYMACalc1 Derivative at a Point,\MYMACalc1\Part III - Derivatives\DefTanLine\DerivPt.html

1 Definitions and Tangent Lines: Derivative at a Point

Limit of a Sequence

Definition MYMACalc1 Precise Limits at Infinity,\MYMACalc1\Part II - Limits and Continuity\Precise\LimatInf.html

1 Precise Limits and Continuity: Precise Limits at Infinity

limit is \(-\infty\)

Definition MYMACalc2 Limits - Definition,\MYMACalc2\Part IV - Sequences & Series\Seq\LimDef.html

2 Sequences: Limits - Definition

limit is \(+\infty\)

Definition MYMACalc2 Limits - Definition,\MYMACalc2\Part IV - Sequences & Series\Seq\LimDef.html

2 Sequences: Limits - Definition

Limits of Functions of \(2\) Variables

Definition MYMACalc3 Precise Limits for Functions of \(2\) Variables (Optional),\MYMACalc3\Part II - Derivatives\LimCont\Prec_2D.html

3 Limits and Continuity: Precise Limits for Functions of \(2\) Variables (Optional)

Limits of Functions of Two Variables

Definition MYMACalc3 Intuitive Limits for Functions of 2 Variables,\MYMACalc3\Part II - Derivatives\LimCont\Lim_2D.html,undefined,\MYMACalc3\Part II - Derivatives\LimCont\Lim_2D_Exist.html

3 Limits and Continuity: Intuitive Limits for Functions of 2 Variables

line integral of a vector field

Definition MYMACalc3 Line Integrals of Vectors,\MYMACalc3\Part I - Geometry & Vectors\LineInt\VectorInt.html

3 Line Integrals: Line Integrals of Vectors

line

3 Lines and Planes: Lines in \(\mathbb{R}^2\) - More on the Normal Equation

line integral of a function

Definition MYMACalc3 Line Integrals of Scalars,\MYMACalc3\Part I - Geometry & Vectors\LineInt\ScalarInt.html

3 Line Integrals: Line Integrals of Scalars

line

Definition MYMACalc1 Parametric Lines,\MYMACalc1\Part I - Pre-Calculus\Vectors\Lines.html

1 Vectors: Parametric Lines

line of longitude

Definition MYMACalc3 3D Spherical Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\3DSphCoord.html

3 Coordinate Systems: 3D Spherical Coordinates

line of latitude

Definition MYMACalc3 3D Spherical Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\3DSphCoord.html

3 Coordinate Systems: 3D Spherical Coordinates

linear combination

Definition MYMACalc3 Linear Combinations,\MYMACalc3\Part I - Geometry & Vectors\Vectors\LinComb.html

3 Vectors: Linear Combinations

linear combination

Definition MYMACalc1 Linear Combinations,\MYMACalc1\Part I - Pre-Calculus\Vectors\LinComb.html

1 Vectors: Linear Combinations

linear

Definition MYMACalc2 What is a Differential Equation?,\MYMACalc2\Part III - Differential Equations\DEIVP\Def.html

2 Differential Equations and Initial Value Problems: What is a Differential Equation?

Linear Approximation with \(1\) Variable

Theorem MYMACalc3 Linear Approximation with \(1\) Variable,\MYMACalc3\Part II - Derivatives\LinApprox\LinApprox1Var.html

3 Linear Approximation: Linear Approximation with \(1\) Variable

Linear Approximation

Theorem MYMACalc1 Linear Approximation,\MYMACalc1\Part III - Derivatives\DiffLinApprox\LinApprox.html

1 Differentials & Linear Approximation: Linear Approximation

Linear Approximation with \(2\) Variables

Theorem MYMACalc3 Linear Approximation with \(2\) Variables,\MYMACalc3\Part II - Derivatives\LinApprox\LinApprox2Var.html

3 Linear Approximation: Linear Approximation with \(2\) Variables

Linear Approximation with \(3\) Variables

Theorem MYMACalc3 Linear Approximation with \(3\) or more Variables,\MYMACalc3\Part II - Derivatives\LinApprox\LinApprox3Var.html

3 Linear Approximation: Linear Approximation with \(3\) or more Variables

linear mass density

Definition MYMACalc3 Review of Center of Mass of a Bar ,\MYMACalc3\Part III - Integrals\RectInt\2DAppsCM.html

3 Multiple Integrals in Rectangular Coordinates: Review of Center of Mass of a Bar

linear density

Definition MYMACalc2 Total Mass,\MYMACalc2\Part II - Applications of Integration\Mass\Mass.html

2 Mass and Center of Mass: Total Mass

linear electric charge density

Definition MYMACalc2 Electric Charge - Bar with Non-Uniform Charge Density,\MYMACalc2\Part II - Applications of Integration\Mass\Charge.html

2 Mass and Center of Mass: Electric Charge - Bar with Non-Uniform Charge Density

local or relative minimum

Definition MYMACalc1 \(2^\text{nd}\) Derivative Test,\MYMACalc1\Part IV - Applications of Derivatives\MaxMin\2ndDerivTest.html

1 Max/Min Problems: \(2^\text{nd}\) Derivative Test

local maximum

Definition MYMACalc3 Functions of \(1\) Variable,\MYMACalc3\Part I - Geometry & Vectors\Functions\MaxMinSaddle.html,Functions of \(2\) Variables,\MYMACalc3\Part I - Geometry & Vectors\Functions\MaxMinSaddle2.html,Local Minima, Local Maxima and Saddle Points of Functions of \(2\) Variables,\MYMACalc3\Part II - Derivatives\MaxMin\MinMaxSaddle.html

3 Functions of Several Variables: Functions of \(1\) Variable

3 Max-Min Problems: Functions of \(2\) Variables

local or relative extrema

Definition MYMACalc3 Local Minima, Local Maxima and Inflection Points of Functions of \(1\) Variable,\MYMACalc3\Part II - Derivatives\MaxMin\MinMaxInfl.html,Local Minima, Local Maxima and Saddle Points of Functions of \(2\) Variables,\MYMACalc3\Part II - Derivatives\MaxMin\MinMaxSaddle.html

3 Max-Min Problems: Local Minima, Local Maxima and Inflection Points of Functions of \(1\) Variable

local minimum

3 Functions of Several Variables: Functions of \(1\) Variable

3 Max-Min Problems: Functions of \(2\) Variables

local or relative minimum

3 Max-Min Problems: Local Minima, Local Maxima and Inflection Points of Functions of \(1\) Variable

local or relative maximum

3 Max-Min Problems: Local Minima, Local Maxima and Inflection Points of Functions of \(1\) Variable

local or relative maximum

Definition MYMACalc1 \(2^\text{nd}\) Derivative Test,\MYMACalc1\Part IV - Applications of Derivatives\MaxMin\2ndDerivTest.html

1 Max/Min Problems: \(2^\text{nd}\) Derivative Test

local or relative extrema

Definition MYMACalc1 \(2^\text{nd}\) Derivative Test,\MYMACalc1\Part IV - Applications of Derivatives\MaxMin\2ndDerivTest.html

1 Max/Min Problems: \(2^\text{nd}\) Derivative Test

locate

Definition MYMACalc3 Vectors as Arrows,\MYMACalc3\Part I - Geometry & Vectors\Vectors\Arrow.html

3 Vectors: Vectors as Arrows

locate

Definition MYMACalc1 Vectors as Arrows,\MYMACalc1\Part I - Pre-Calculus\Vectors\Arrow.html

1 Vectors: Vectors as Arrows

located scalar

Definition MYMACalc3 Free vs. Located,\MYMACalc3\Part I - Geometry & Vectors\Vectors\FreeVsLocated.html

3 Vectors: Free vs. Located

located vector

Definition MYMACalc3 Free vs. Located,\MYMACalc3\Part I - Geometry & Vectors\Vectors\FreeVsLocated.html

3 Vectors: Free vs. Located

logistic growth

Definition MYMACalc2 Logistic Growth,\MYMACalc2\Part III - Differential Equations\DEApps\Logistic.html

2 Applications of Differential Equations: Logistic Growth

logistic growth model

Definition MYMACalc2 Logistic Growth,\MYMACalc2\Part III - Differential Equations\DEApps\Logistic.html

2 Applications of Differential Equations: Logistic Growth

lower bound

Definition MYMACalc2 Bounded Sequences,\MYMACalc2\Part IV - Sequences & Series\Seq\Bnd.html,Left, Right and Middle Riemann Sums - For a Known Antiderivative,\MYMACalc2\Part I - Techniques of Integration\NumInt\LRMKnown.html

2 Sequences: Bounded Sequences

2 Numerical Integration: Left, Right and Middle Riemann Sums - For a Known Antiderivative

LPMD's

Definition MYMACalc3 Second Derivative Test with More Variables (Optional),\MYMACalc3\Part II - Derivatives\MaxMin\SecondDerTest2.html

3 Max-Min Problems: Second Derivative Test with More Variables (Optional)

Maclaurin Series Theorem

Theorem MYMACalc2 Taylor Series Definition,\MYMACalc2\Part IV - Sequences & Series\Taylor\Def.html

2 Taylor Series: Taylor Series Definition

Maclaurin series

Definition MYMACalc2 Taylor Series Definition,\MYMACalc2\Part IV - Sequences & Series\Taylor\Def.html

2 Taylor Series: Taylor Series Definition

magnitude

Definition MYMACalc1 Vectors as Arrows,\MYMACalc1\Part I - Pre-Calculus\Vectors\Arrow.html,Direction,\MYMACalc1\Part I - Pre-Calculus\Vectors\Dir.html,Magnitude,\MYMACalc1\Part I - Pre-Calculus\Vectors\Mag.html

1 Vectors: Vectors as Arrows

magnitude

Definition MYMACalc3 Vectors as Arrows,\MYMACalc3\Part I - Geometry & Vectors\Vectors\Arrow.html,Direction,\MYMACalc3\Part I - Geometry & Vectors\Vectors\Dir.html,Magnitude,\MYMACalc3\Part I - Geometry & Vectors\Vectors\Mag.html

3 Vectors: Vectors as Arrows

magnitude

Definition MYMACalc2 Complex Methods (Optional),\MYMACalc2\Part I - Techniques of Integration\ParFrac\Coeffs2Complex.html

2 Partial Fractions: Complex Methods (Optional)

mass density

Definition MYMACalc3 The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian,\MYMACalc3\Part II - Derivatives\DivCurlPots\OpDivGrad.html

3 Divergence, Curl and Potentials: The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian

mass

Definition MYMACalc3 Review of Center of Mass of a Bar ,\MYMACalc3\Part III - Integrals\RectInt\2DAppsCM.html,Applications of Double Integrals - Center of Mass,\MYMACalc3\Part III - Integrals\RectInt\2DAppsCM.html,Center of Mass,\MYMACalc3\Part III - Integrals\SurfInt\CM.html

3 Multiple Integrals in Rectangular Coordinates: Review of Center of Mass of a Bar

3 Parametric Surfaces and Surface Integrals: Applications of Double Integrals - Center of Mass

matrix is diagonal

Definition MYMACalc3 Properties of Determinants,\MYMACalc3\Part I - Geometry & Vectors\Cross\DetProp.html

3 Cross Product: Properties of Determinants

Mean Value Theorem for Derivatives

Theorem MYMACalc2 undefined,\MYMACalc2\Part IV - Sequences & Series\Taylor\RemainderPf.html

2 Taylor Series: undefined

Middle Riemann Sum Error and Bound Theorem

Theorem MYMACalc2 Error Bounds - Trapezoid Rule and Middle Riemann Sum,\MYMACalc2\Part I - Techniques of Integration\NumInt\TrapMidErr.html

2 Numerical Integration: Error Bounds - Trapezoid Rule and Middle Riemann Sum

Midpoint of a Line Segment

Theorem MYMACalc3 Distance Formula in 2D,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DDistance.html,Distance Formula in 3D,\MYMACalc3\Part I - Geometry & Vectors\Coords\3DDistance.html

3 Coordinate Systems: Distance Formula in 2D

mixed second partials

Definition MYMACalc3 Higher Derivatives,\MYMACalc3\Part II - Derivatives\Higher\HigherDer.html

3 Higher Order Derivatives: Higher Derivatives

Mixing problems

Definition MYMACalc2 Mixing Problems,\MYMACalc2\Part III - Differential Equations\DEApps\Mixing.html

2 Applications of Differential Equations: Mixing Problems

Moment of Inertia of a Bar with Non-Uniform Density

Theorem MYMACalc2 Moment of Inertia - Bar with Non-Uniform Density,\MYMACalc2\Part II - Applications of Integration\Mass\MomInertia.html

2 Mass and Center of Mass: Moment of Inertia - Bar with Non-Uniform Density

moment about the \(x\)-axis

Definition MYMACalc3 Applications of Double Integrals - Center of Mass,\MYMACalc3\Part III - Integrals\RectInt\2DAppsCM.html

3 Multiple Integrals in Rectangular Coordinates: Applications of Double Integrals - Center of Mass

moment

Definition MYMACalc3 Applications of Double Integrals - Centroid of a Region,\MYMACalc3\Part III - Integrals\RectInt\2DAppsCentroid.html, Review of Center of Mass of a Bar ,\MYMACalc3\Part III - Integrals\RectInt\2DAppsCM.html,Applications of Double Integrals - Center of Mass,\MYMACalc3\Part III - Integrals\RectInt\2DAppsCM.html

3 Multiple Integrals in Rectangular Coordinates: Applications of Double Integrals - Centroid of a Region

moment of inertia

Definition MYMACalc2 Moment of Inertia - Bar with Non-Uniform Density,\MYMACalc2\Part II - Applications of Integration\Mass\MomInertia.html

2 Mass and Center of Mass: Moment of Inertia - Bar with Non-Uniform Density

moment about the \(y\)-axis

Definition MYMACalc3 Applications of Double Integrals - Center of Mass,\MYMACalc3\Part III - Integrals\RectInt\2DAppsCM.html

3 Multiple Integrals in Rectangular Coordinates: Applications of Double Integrals - Center of Mass

moments of the area

Definition MYMACalc3 Centroid,\MYMACalc3\Part III - Integrals\SurfInt\Centroid.html

3 Parametric Surfaces and Surface Integrals: Centroid

moments of the mass

Definition MYMACalc3 Center of Mass,\MYMACalc3\Part III - Integrals\SurfInt\CM.html

3 Parametric Surfaces and Surface Integrals: Center of Mass

monkey saddle

Definition MYMACalc3 Functions of \(2\) Variables,\MYMACalc3\Part I - Geometry & Vectors\Functions\MaxMinSaddle2.html

3 Functions of Several Variables: Functions of \(2\) Variables

monotonic

Definition MYMACalc2 Monotonic Sequences,\MYMACalc2\Part IV - Sequences & Series\Seq\Mono.html

2 Sequences: Monotonic Sequences

Multiple of a Row (Row Operation II)*

Theorem MYMACalc3 Properties of Determinants,\MYMACalc3\Part I - Geometry & Vectors\Cross\DetProp.html

3 Cross Product: Properties of Determinants

Multiplication of Power Series by Polynomials

Theorem MYMACalc2 Multiplication by Polynomials,\MYMACalc2\Part IV - Sequences & Series\PowSer\Mult.html

2 Power Series: Multiplication by Polynomials

multiplicative constant of integration

Definition MYMACalc2 Exponential Growth and Decay,\MYMACalc2\Part III - Differential Equations\DEApps\Exp.html

2 Applications of Differential Equations: Exponential Growth and Decay

multiplicity

Definition MYMACalc2 General Decompositions,\MYMACalc2\Part I - Techniques of Integration\ParFrac\Decomp.html

2 Partial Fractions: General Decompositions

\(n\)D Spherical Coordinates

Definition MYMACalc3 Cylindrical and Spherical Coordinates in Higher Dimensions (Optional),\MYMACalc3\Part I - Geometry & Vectors\Coords\nDCylSphCoord.html

3 Coordinate Systems: Cylindrical and Spherical Coordinates in Higher Dimensions (Optional)

\(n\)D Cylindrical Coordinates

Definition MYMACalc3 Cylindrical and Spherical Coordinates in Higher Dimensions (Optional),\MYMACalc3\Part I - Geometry & Vectors\Coords\nDCylSphCoord.html

3 Coordinate Systems: Cylindrical and Spherical Coordinates in Higher Dimensions (Optional)

nearby

Definition MYMACalc3 Functions of \(1\) Variable,\MYMACalc3\Part I - Geometry & Vectors\Functions\MaxMinSaddle.html,Functions of \(2\) Variables,\MYMACalc3\Part I - Geometry & Vectors\Functions\MaxMinSaddle2.html,Local Minima, Local Maxima and Inflection Points of Functions of \(1\) Variable,\MYMACalc3\Part II - Derivatives\MaxMin\MinMaxInfl.html,Local Minima, Local Maxima and Saddle Points of Functions of \(2\) Variables,\MYMACalc3\Part II - Derivatives\MaxMin\MinMaxSaddle.html

3 Functions of Several Variables: Functions of \(1\) Variable

3 Max-Min Problems: Functions of \(2\) Variables

negative infinity

Definition MYMACalc1 Precise Limits at Infinity,\MYMACalc1\Part II - Limits and Continuity\Precise\LimatInf.html

1 Precise Limits and Continuity: Precise Limits at Infinity

negative

Definition MYMACalc2 Overview,\MYMACalc2\Part IV - Sequences & Series\SerPos\Overview.html

2 Convergence of General Series: Overview

2 Convergence of Positive Series:

negative of a vector \(\vec v\)

Definition MYMACalc1 Properties,\MYMACalc1\Part I - Pre-Calculus\Vectors\DotProp.html

1 Dot Product: Properties

negative infinity

Definition MYMACalc2 Precise Definiton of Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\PrecDef.html,Integrals Improper at an Infinite Endpoint,\MYMACalc2\Part I - Techniques of Integration\Improper\Inf.html

2 Sequences: Precise Definiton of Limits

2 Improper Integrals: Integrals Improper at an Infinite Endpoint

negative of a vector \(\vec v\)

Definition MYMACalc3 Properties,\MYMACalc3\Part I - Geometry & Vectors\Dot\DotProp.html

3 Dot Product: Properties

Net Electric Charge on a Bar with Non-Uniform Charge Density

Theorem MYMACalc2 Electric Charge - Bar with Non-Uniform Charge Density,\MYMACalc2\Part II - Applications of Integration\Mass\Charge.html

2 Mass and Center of Mass: Electric Charge - Bar with Non-Uniform Charge Density

net charge

Definition MYMACalc2 Electric Charge - Bar with Non-Uniform Charge Density,\MYMACalc2\Part II - Applications of Integration\Mass\Charge.html

2 Mass and Center of Mass: Electric Charge - Bar with Non-Uniform Charge Density

net electric charge

Definition MYMACalc2 Electric Charge - Bar with Non-Uniform Charge Density,\MYMACalc2\Part II - Applications of Integration\Mass\Charge.html

2 Mass and Center of Mass: Electric Charge - Bar with Non-Uniform Charge Density

Newton's Law of Heating and Cooling

Theorem MYMACalc2 Newtonian Heating and Cooling,\MYMACalc2\Part III - Differential Equations\DEApps\Cooling.html

2 Applications of Differential Equations: Newtonian Heating and Cooling

Newton's Law of Gravity

Definition MYMACalc3 The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian,\MYMACalc3\Part II - Derivatives\DivCurlPots\OpDivGrad.html

3 Divergence, Curl and Potentials: The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian

Newton's Second Law of Rotational Motion

Definition MYMACalc3 Application - Balancing Torques,\MYMACalc3\Part I - Geometry & Vectors\Cross\BalTorques.html

3 Cross Product: Application - Balancing Torques

Non-Existence of a Scalar Potential

Theorem MYMACalc3 Non-Existence of a Scalar Potential,\MYMACalc3\Part II - Derivatives\DivCurlPots\NoScalPot.html

3 Divergence, Curl and Potentials: Non-Existence of a Scalar Potential

Non-Existence of a Vector Potential

Theorem MYMACalc3 Non-Existence of a Vector Potential,\MYMACalc3\Part II - Derivatives\DivCurlPots\NoVecPot.html

3 Divergence, Curl and Potentials: Non-Existence of a Vector Potential

non-parametric equations

Definition MYMACalc3 Planes - Non-Parametric Equations,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\PlaneNonParam1.html

3 Lines and Planes: Planes - Non-Parametric Equations

Non-Parametric Equation of a Line

Theorem MYMACalc3 Lines - Non-Parametric Equations,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\LineNonParam1.html

3 Lines and Planes: Lines - Non-Parametric Equations

non-parametric equation of the line

Definition MYMACalc3 Lines - Non-Parametric Equations,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\LineNonParam1.html

3 Lines and Planes: Lines - Non-Parametric Equations

Non-Uniqueness of Antiderivatives

Theorem MYMACalc2 Non-Uniqueness of Antiderivatives,\MYMACalc2\Part I - Techniques of Integration\AntiDer\NonUniq.html

2 Antiderivatives: Non-Uniqueness of Antiderivatives

normal equation

Definition MYMACalc3 Lines in \(\mathbb{R}^2\) - More on the Normal Equation,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\LineNonParam3.html,Planes in \(\mathbb{R}^3\) - More on the Normal Equation,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\PlaneNonParam2.html

3 Lines and Planes: Lines in \(\mathbb{R}^2\) - More on the Normal Equation

normal form

Definition MYMACalc3 Lines in \(\mathbb{R}^2\) - Non-Parametric Equations,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\LineNonParam2.html,Planes - Non-Parametric Equations,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\PlaneNonParam1.html

3 Lines and Planes: Lines in \(\mathbb{R}^2\) - Non-Parametric Equations

normal acceleration

Definition MYMACalc3 Tangential and Normal Acceleration,\MYMACalc3\Part I - Geometry & Vectors\CurveProps\TNAcc.html

3 Properties of Curves: Tangential and Normal Acceleration

normal differential of arc length

Definition MYMACalc3 Normal Line Integrals in \(\mathbb{R}^2\),\MYMACalc3\Part I - Geometry & Vectors\LineInt\NormalInt.html

3 Line Integrals: Normal Line Integrals in \(\mathbb{R}^2\)

normal line integral of a vector field

Definition MYMACalc3 Normal Line Integrals in \(\mathbb{R}^2\),\MYMACalc3\Part I - Geometry & Vectors\LineInt\NormalInt.html

3 Line Integrals: Normal Line Integrals in \(\mathbb{R}^2\)

normal vector

Definition MYMACalc3 Normal Vector,\MYMACalc3\Part III - Integrals\SurfInt\NormalVec2.html

3 Parametric Surfaces and Surface Integrals: Normal Vector

number of terms

Definition MYMACalc2 Geometric Series - Finite,\MYMACalc2\Part IV - Sequences & Series\Ser\GeomFin.html

2 Series: Geometric Series - Finite

octants

Definition MYMACalc3 3D Rectangular Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\3DRectCoord.html

3 Coordinate Systems: 3D Rectangular Coordinates

optimize

Definition MYMACalc3 Constrained Max-Min Problems,\MYMACalc3\Part II - Derivatives\MaxMin\Constraint.html

3 Max-Min Problems: Constrained Max-Min Problems

optimized function

Definition MYMACalc3 Constrained Max-Min Problems,\MYMACalc3\Part II - Derivatives\MaxMin\Constraint.html

3 Max-Min Problems: Constrained Max-Min Problems

order

Definition MYMACalc2 What is a Differential Equation?,\MYMACalc2\Part III - Differential Equations\DEIVP\Def.html

2 Differential Equations and Initial Value Problems: What is a Differential Equation?

ordered triple notation

Definition MYMACalc3 \(ijk\) Notation,\MYMACalc3\Part I - Geometry & Vectors\Vectors\ijkNote.html

3 Vectors: \(ijk\) Notation

ordered triple notation

Definition MYMACalc1 \(\hat\imath\hat\jmath\) Notation,\MYMACalc1\Part I - Pre-Calculus\Vectors\ijNote.html

1 Vectors: \(\hat\imath\hat\jmath\) Notation

orientable

Definition MYMACalc3 Vector Surface Integrals,\MYMACalc3\Part III - Integrals\SurfInt\VecSurfInt.html

3 Parametric Surfaces and Surface Integrals: Vector Surface Integrals

orientation

Definition MYMACalc3 Vector Surface Integrals,\MYMACalc3\Part III - Integrals\SurfInt\VecSurfInt.html

3 Parametric Surfaces and Surface Integrals: Vector Surface Integrals

orientation of the curve

Definition MYMACalc3 Flow and Circulation,\MYMACalc3\Part I - Geometry & Vectors\LineInt\FlowCirc.html

3 Line Integrals: Flow and Circulation

oriented

Definition MYMACalc3 Vector Surface Integrals,\MYMACalc3\Part III - Integrals\SurfInt\VecSurfInt.html

3 Parametric Surfaces and Surface Integrals: Vector Surface Integrals

orienteering

Definition MYMACalc3 Application: Orienteering,\MYMACalc3\Part I - Geometry & Vectors\Vectors\Orient.html

3 Vectors: Application: Orienteering

origin

Definition MYMACalc3 2D Rectangular Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DRectCoord.html

3 Coordinate Systems: 2D Rectangular Coordinates

original series

Definition MYMACalc2 Overview,\MYMACalc2\Part IV - Sequences & Series\SerPos\Overview.html

2 Convergence of Positive Series: Overview

oscillatory divergent

Definition MYMACalc2 Limits - Definition,\MYMACalc2\Part IV - Sequences & Series\Seq\LimDef.html

2 Sequences: Limits - Definition

osculating circle

Definition MYMACalc3 Curvature,\MYMACalc3\Part I - Geometry & Vectors\CurveProps\Curvature.html

3 Properties of Curves: Curvature

outer

Definition MYMACalc3 Chain Rule with \(1\) Intermediate Variable,\MYMACalc3\Part II - Derivatives\Chain\ChainRule1.html

3 Chain Rule: Chain Rule with \(1\) Intermediate Variable

outer

Definition MYMACalc1 Chain Rule,\MYMACalc1\Part III - Derivatives\Chain\Chain.html

1 Chain Rule & Implicit Differentiation: Chain Rule

output tolerance

3 Limits and Continuity: Precise Limits for Functions of \(1\) Variable (Optional Review)

output tolerance

Definition MYMACalc2 Precise Definiton of Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\PrecDef.html

2 Sequences: Precise Definiton of Limits

output bound

Definition MYMACalc1 Precise Infinite Limits,\MYMACalc1\Part II - Limits and Continuity\Precise\InfLim.html

1 Precise Limits and Continuity: Precise Infinite Limits

output tolerance

1 Precise Limits and Continuity: Precise Limits at Infinity

\((p,q)\)-moment

Definition MYMACalc3 Applications of Double Integrals - Centroid of a Region,\MYMACalc3\Part III - Integrals\RectInt\2DAppsCentroid.html

3 Multiple Integrals in Rectangular Coordinates: Applications of Double Integrals - Centroid of a Region

\(p\)-series

Definition MYMACalc2 The Integral Test,\MYMACalc2\Part IV - Sequences & Series\SerPos\IntegTest.html,The \(p\)-Series,\MYMACalc2\Part IV - Sequences & Series\SerPos\pSerTest.html

2 Convergence of Positive Series: The Integral Test

parabola

Definition MYMACalc3 Quadratic Curves - Part 2,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\CrvR2Quad2.html

3 Curves and Surfaces: Quadratic Curves - Part 2

parabolic cylinders

Definition MYMACalc3 Quadratic Surfaces - Part 2,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3Quad2.html

3 Curves and Surfaces: Quadratic Surfaces - Part 2

parabolic cylinder

Definition MYMACalc3 Quadratic Surfaces - Part 2,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3Quad2.html

3 Curves and Surfaces: Quadratic Surfaces - Part 2

paraboloids

Definition MYMACalc3 Quadratic Surfaces - Part 2,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3Quad2.html

3 Curves and Surfaces: Quadratic Surfaces - Part 2

Parallel and Perpenducular Scalar Projections

Theorem MYMACalc3 Scalar Projections,\MYMACalc3\Part I - Geometry & Vectors\Dot\ProjScalar.html

3 Dot Product: Scalar Projections

Parallel Vector Projection

Theorem MYMACalc1 Vector Projections,\MYMACalc1\Part I - Pre-Calculus\Vectors\ProjVector.html

1 Vectors: Vector Projections

Parallel Vector Projection

Theorem MYMACalc3 Vector Projections,\MYMACalc3\Part I - Geometry & Vectors\Dot\ProjVector.html

3 Dot Product: Vector Projections

Parallel and Perpenducular Scalar Projections

Theorem MYMACalc1 Scalar Projections,\MYMACalc1\Part I - Pre-Calculus\Vectors\ProjScalar.html

1 Vectors: Scalar Projections

Parallelogram Method

Theorem MYMACalc1 Vector Addition - Geometric,\MYMACalc1\Part I - Pre-Calculus\Vectors\VecAddGeom.html

1 Vectors: Vector Addition - Geometric

Parallelogram Method

Theorem MYMACalc3 Vector Addition: Geometric Construction,\MYMACalc3\Part I - Geometry & Vectors\Vectors\VecAddGeom.html

3 Vectors: Vector Addition: Geometric Construction

parameter

3 Curves and Surfaces: Curves in \(\mathbb{R}^2\)

3 Lines and Planes: Curves in \(\mathbb{R}^3\)

parameter

Definition MYMACalc1 Parametric Curves,\MYMACalc1\Part I - Pre-Calculus\Vectors\Curves.html,Parametric Lines,\MYMACalc1\Part I - Pre-Calculus\Vectors\Lines.html

1 Vectors: Parametric Curves

parameters

Definition MYMACalc3 Surfaces in \(\mathbb{R}^3\),\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3.html,Planes - Parametric Equations,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\PlaneParam1.html

3 Curves and Surfaces: Surfaces in \(\mathbb{R}^3\)

3 Lines and Planes: Planes - Parametric Equations

Parametric Equation of a Line

Theorem MYMACalc1 Parametric Lines,\MYMACalc1\Part I - Pre-Calculus\Vectors\Lines.html

1 Vectors: Parametric Lines

parametric equation of the plane

Definition MYMACalc3 Planes - Parametric Equations,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\PlaneParam1.html

3 Lines and Planes: Planes - Parametric Equations

parametric curve

Definition MYMACalc1 Parametric Curves,\MYMACalc1\Part I - Pre-Calculus\Vectors\Curves.html

1 Vectors: Parametric Curves

parametric equation

Definition MYMACalc3 Lines - Parametric Equations,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\LineParam1.html,Planes - Parametric Equations,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\PlaneParam1.html

3 Lines and Planes: Lines - Parametric Equations

parametric equation of the line

Definition MYMACalc3 Lines - Parametric Equations,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\LineParam1.html

3 Lines and Planes: Lines - Parametric Equations

Parametric Equation of a Line

Theorem MYMACalc3 Lines - Parametric Equations,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\LineParam1.html

3 Lines and Planes: Lines - Parametric Equations

Parametric Equation of a Plane

Theorem MYMACalc3 Planes - Parametric Equations,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\PlaneParam1.html

3 Lines and Planes: Planes - Parametric Equations

parametric equation of the line

Definition MYMACalc1 Parametric Lines,\MYMACalc1\Part I - Pre-Calculus\Vectors\Lines.html

1 Vectors: Parametric Lines

parametric equation

Definition MYMACalc1 Parametric Lines,\MYMACalc1\Part I - Pre-Calculus\Vectors\Lines.html

1 Vectors: Parametric Lines

parametric surface

Definition MYMACalc3 Surfaces in \(\mathbb{R}^3\),\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3.html,Introduction to Parametric Surfaces,\MYMACalc3\Part III - Integrals\SurfInt\PosPlots.html,Position,\MYMACalc3\Part III - Integrals\SurfInt\PosPlots.html

3 Curves and Surfaces: Surfaces in \(\mathbb{R}^3\)

3 Parametric Surfaces and Surface Integrals: Introduction to Parametric Surfaces

parametric curve

Definition MYMACalc3 Curves in \(\mathbb{R}^2\),\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\CrvR2.html,Curves in \(\mathbb{R}^3\),\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\CrvR3.html,Introduction to Parametric Surfaces,\MYMACalc3\Part III - Integrals\SurfInt\PosPlots.html,Position,\MYMACalc3\Part III - Integrals\SurfInt\PosPlots.html

3 Curves and Surfaces: Curves in \(\mathbb{R}^2\)

3 Parametric Surfaces and Surface Integrals: Curves in \(\mathbb{R}^3\)

parametric curve

Definition MYMACalc2 Arc Length of a Parametric Curve,\MYMACalc2\Part II - Applications of Integration\ArcSurf\ArcParam.html,Parametric Curves,\MYMACalc2\Part II - Applications of Integration\ArcSurf\ParamCrv.html

2 Arc Length and Surface Area: Arc Length of a Parametric Curve

Parametrization Method

Theorem MYMACalc3 Multiple Constraint Problems (Optional),\MYMACalc3\Part II - Derivatives\MaxMin\MultConstraint.html

3 Max-Min Problems: Multiple Constraint Problems (Optional)

parametrized region

Definition MYMACalc3 Introduction to Parametric Surfaces,\MYMACalc3\Part III - Integrals\SurfInt\PosPlots.html

3 Parametric Surfaces and Surface Integrals: Introduction to Parametric Surfaces

Parametrizing the Graph of a Function

Theorem MYMACalc2 Parametric Curves,\MYMACalc2\Part II - Applications of Integration\ArcSurf\ParamCrv.html

2 Arc Length and Surface Area: Parametric Curves

partial derivatives

Definition MYMACalc3 Algebraic Definition of Partial Derivatives,\MYMACalc3\Part II - Derivatives\ParDerTanPlane\ParDerAlg.html

3 Partial Derivatives and Tangent Planes: Algebraic Definition of Partial Derivatives

partial

Definition MYMACalc3 Computation,\MYMACalc3\Part II - Derivatives\ParDerTanPlane\Compute.html

3 Partial Derivatives and Tangent Planes: Computation

partial derivative

Definition MYMACalc3 Computation,\MYMACalc3\Part II - Derivatives\ParDerTanPlane\Compute.html

3 Partial Derivatives and Tangent Planes: Computation

partition points

Definition MYMACalc3 Riemann Sum Definition of Single Integrals (Review),\MYMACalc3\Part III - Integrals\RiemInt\1DRiem.html

3 Multiple Integrals as Riemann Sums: Riemann Sum Definition of Single Integrals (Review)

path

Definition MYMACalc2 Parametric Curves,\MYMACalc2\Part II - Applications of Integration\ArcSurf\ParamCrv.html

2 Arc Length and Surface Area: Parametric Curves

path independent integrals

Definition MYMACalc3 Application - Path Independence,\MYMACalc3\Part IV - Theorems\ThmFTCC\ApplPathIndep.html

3 Fundamental Theorem of Calculus for Curves: Application - Path Independence

Perpendicular Vector Projection

Theorem MYMACalc1 Vector Projections,\MYMACalc1\Part I - Pre-Calculus\Vectors\ProjVector.html

1 Vectors: Vector Projections

Perpendicular Vector Projection

Theorem MYMACalc3 Vector Projections,\MYMACalc3\Part I - Geometry & Vectors\Dot\ProjVector.html

3 Dot Product: Vector Projections

\(\phi\)-curve

Definition MYMACalc3 3D Spherical Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\3DSphCoord.html

3 Coordinate Systems: 3D Spherical Coordinates

pivot point

Definition MYMACalc3 Application - Balancing Torques,\MYMACalc3\Part I - Geometry & Vectors\Cross\BalTorques.html

3 Cross Product: Application - Balancing Torques

pivot point

Definition MYMACalc2 Moment of Inertia - Bar with Non-Uniform Density,\MYMACalc2\Part II - Applications of Integration\Mass\MomInertia.html

2 Mass and Center of Mass: Moment of Inertia - Bar with Non-Uniform Density

planar curve

Definition MYMACalc3 Curves in \(\mathbb{R}^2\),\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\CrvR2.html

3 Curves and Surfaces: Curves in \(\mathbb{R}^2\)

planar curve

Definition MYMACalc1 Parametric Curves,\MYMACalc1\Part I - Pre-Calculus\Vectors\Curves.html

1 Vectors: Parametric Curves

plane

Definition MYMACalc3 Planes - Parametric Equations,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\PlaneParam1.html

3 Lines and Planes: Planes - Parametric Equations

plot

Definition MYMACalc3 Plot,\MYMACalc3\Part III - Integrals\SurfInt\PosPlots.html

3 Parametric Surfaces and Surface Integrals: Plot

point-slope formula

Definition MYMACalc3 Lines in \(\mathbb{R}^2\) - Non-Parametric Equations,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\LineNonParam2.html

3 Lines and Planes: Lines in \(\mathbb{R}^2\) - Non-Parametric Equations

Poisson Equation

Definition MYMACalc3 The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian,\MYMACalc3\Part II - Derivatives\DivCurlPots\OpDivGrad.html

3 Divergence, Curl and Potentials: The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian

polar differential of area

Definition MYMACalc3 Polar Coordinates - Grid Cell,\MYMACalc3\Part III - Integrals\CurvInt\Polar-Grid.html

3 Multiple Integrals in Curvilinear Coordinates: Polar Coordinates - Grid Cell

polar angle

Definition MYMACalc3 2D Polar Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DPolarCoord.html,3D Spherical Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\3DSphCoord.html,Cylindrical and Spherical Coordinates in Higher Dimensions (Optional),\MYMACalc3\Part I - Geometry & Vectors\Coords\nDCylSphCoord.html

3 Coordinate Systems: 2D Polar Coordinates

Polar Coordinates

Definition MYMACalc3 2D Polar Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DPolarCoord.html

3 Coordinate Systems: 2D Polar Coordinates

polar graph of an equation

Definition MYMACalc2 Graphs of Polar Equations,\MYMACalc2\Part II - Applications of Integration\Polar\Graph.html

2 Polar Coordinates: Graphs of Polar Equations

polar angle

Definition MYMACalc2 Polar Coordinate System,\MYMACalc2\Part II - Applications of Integration\Polar\Def.html

2 Polar Coordinates: Polar Coordinate System

polar rectangle

Definition MYMACalc3 Polar Coordinates - Grid Cell,\MYMACalc3\Part III - Integrals\CurvInt\Polar-Grid.html

3 Multiple Integrals in Curvilinear Coordinates: Polar Coordinates - Grid Cell

polar equation

Definition MYMACalc2 Polar Equations,\MYMACalc2\Part II - Applications of Integration\Polar\PolarEq.html

2 Polar Coordinates: Polar Equations

polar equation

Definition MYMACalc3 Polar Equations,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DPolarEq.html

3 Polar Coordinates: Polar Equations

Polar Angle Formula

Theorem MYMACalc3 2D Converting between Rectangular and Polar,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DPolarConvert.html

3 Coordinate Systems: 2D Converting between Rectangular and Polar

Polar Coordinates

Definition MYMACalc2 Polar Coordinate System,\MYMACalc2\Part II - Applications of Integration\Polar\Def.html

2 Polar Coordinates: Polar Coordinate System

Polar Angle Formula

Theorem MYMACalc2 Converting Between Rectangular and Polar Coordinates,\MYMACalc2\Part II - Applications of Integration\Polar\Convert.html

2 Polar Coordinates: Converting Between Rectangular and Polar Coordinates

polar graph

Definition MYMACalc3 2D Polar Plots,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DPolarPlot.html

3 Coordinate Systems: 2D Polar Plots

position equation

Definition MYMACalc2 Falling near the Earth,\MYMACalc2\Part III - Differential Equations\DEApps\FreeFall.html,Falling with Air Resistance,\MYMACalc2\Part III - Differential Equations\DEApps\TermVel.html

2 Applications of Differential Equations: Falling near the Earth

position vector

Definition MYMACalc2 Parametric Curves,\MYMACalc2\Part II - Applications of Integration\ArcSurf\ParamCrv.html

2 Arc Length and Surface Area: Parametric Curves

position vector

Definition MYMACalc3 Application - Balancing Torques,\MYMACalc3\Part I - Geometry & Vectors\Cross\BalTorques.html,Vector Functions: Position and Plots,\MYMACalc3\Part I - Geometry & Vectors\CurveProps\VecFnsPosPlot.html,Vectors as Arrows,\MYMACalc3\Part I - Geometry & Vectors\Vectors\Arrow.html

3 Cross Product: Application - Balancing Torques

3 Properties of Curves: Vector Functions: Position and Plots

3 Vectors: Vectors as Arrows

position

Definition MYMACalc3 Curves in \(\mathbb{R}^2\),\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\CrvR2.html,Curves in \(\mathbb{R}^3\),\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\CrvR3.html,Surfaces in \(\mathbb{R}^3\),\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3.html,Lines - Parametric Equations,\MYMACalc3\Part I - Geometry & Vectors\LinePlane\LineParam1.html,Position,\MYMACalc3\Part III - Integrals\SurfInt\PosPlots.html

3 Curves and Surfaces: Curves in \(\mathbb{R}^2\)

3 Lines and Planes: Curves in \(\mathbb{R}^3\)

3 Parametric Surfaces and Surface Integrals: Surfaces in \(\mathbb{R}^3\)

position vector

Definition MYMACalc1 Vectors as Arrows,\MYMACalc1\Part I - Pre-Calculus\Vectors\Arrow.html,Position Vector,\MYMACalc1\Part III - Derivatives\ParamCurves\Position.html

1 Vectors: Vectors as Arrows

1 Parametric Curves: Position Vector

position

Definition MYMACalc1 Parametric Curves,\MYMACalc1\Part I - Pre-Calculus\Vectors\Curves.html,Parametric Lines,\MYMACalc1\Part I - Pre-Calculus\Vectors\Lines.html

1 Vectors: Parametric Curves

positive infinity

Definition MYMACalc1 Precise Limits at Infinity,\MYMACalc1\Part II - Limits and Continuity\Precise\LimatInf.html

1 Precise Limits and Continuity: Precise Limits at Infinity

positive

Definition MYMACalc2 Overview,\MYMACalc2\Part IV - Sequences & Series\SerPos\Overview.html

2 Convergence of General Series: Overview

2 Convergence of Positive Series:

positive infinity

Definition MYMACalc2 Precise Definiton of Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\PrecDef.html

2 Sequences: Precise Definiton of Limits

potential energy

Definition MYMACalc3 Application - Work,\MYMACalc3\Part IV - Theorems\ThmFTCC\ApplWork.html

3 Fundamental Theorem of Calculus for Curves: Application - Work

power series

Definition MYMACalc2 What is a Power Series?,\MYMACalc2\Part IV - Sequences & Series\PowSer\Def.html

2 Power Series: What is a Power Series?

Power Sequences

1 Computing Limits: Limits of Special Functions

1 Precise Limits and Continuity: Limits of Non-Linear Functions

Power Sequences

Theorem MYMACalc2 Special Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\LimSpec.html,Precise Special Limits,\MYMACalc2\Part IV - Sequences & Series\Seq\PrecSpec.html

2 Sequences: Special Limits

power series

Definition MYMACalc2 Radius of Convergence,\MYMACalc2\Part IV - Sequences & Series\PowSer\Radius.html

2 Power Series: Radius of Convergence

principle diagonal

Definition MYMACalc3 Method of Diagonals,\MYMACalc3\Part I - Geometry & Vectors\Cross\DetDiag.html

3 Cross Product: Method of Diagonals

probability density function (PDF)

Definition MYMACalc2 Exercises,\MYMACalc2\Part I - Techniques of Integration\Improper\x.html

2 Improper Integrals: Exercises

probability

Definition MYMACalc3 Average Value,\MYMACalc3\Part I - Geometry & Vectors\LineInt\Ave.html

3 Line Integrals: Average Value

probability distribution

Definition MYMACalc3 Average Value,\MYMACalc3\Part I - Geometry & Vectors\LineInt\Ave.html

3 Line Integrals: Average Value

Procedure

Theorem MYMACalc2 Substitutions for \(a^2x^2+b^2\) and \(a^2x^2-b^2\),\MYMACalc2\Part I - Techniques of Integration\TrigSubs\Coef.html,Substitutions for \(1-x^2\) (or \(x^2-1\)) - Sine Substitutions,\MYMACalc2\Part I - Techniques of Integration\TrigSubs\Sin.html,Substitutions for \(x^2-1\) (or \(1-x^2\)) - Secant Substitutions,\MYMACalc2\Part I - Techniques of Integration\TrigSubs\Sec.html,Substitutions for \(x^2+1\) - Tangent Substitutions,\MYMACalc2\Part I - Techniques of Integration\TrigSubs\Tan.html

2 Trigonometric Substitutions: Substitutions for \(a^2x^2+b^2\) and \(a^2x^2-b^2\)

projection of the vector \(\vec v\) perpendicular to the direction of \(\vec u\)

Definition MYMACalc3 Vector Projections,\MYMACalc3\Part I - Geometry & Vectors\Dot\ProjVector.html

3 Dot Product: Vector Projections

projection of the vector \(\vec v\) parallel to the direction of \(\vec u\)

Definition MYMACalc3 Vector Projections,\MYMACalc3\Part I - Geometry & Vectors\Dot\ProjVector.html

3 Dot Product: Vector Projections

projection of the vector \(\vec v\) parallel to the direction of \(\vec u\)

Definition MYMACalc1 Vector Projections,\MYMACalc1\Part I - Pre-Calculus\Vectors\ProjVector.html

1 Vectors: Vector Projections

projection of the vector \(\vec v\) perpendicular to the direction of \(\vec u\)

Definition MYMACalc1 Vector Projections,\MYMACalc1\Part I - Pre-Calculus\Vectors\ProjVector.html

1 Vectors: Vector Projections

Properties of the Gradient

Theorem MYMACalc3 Properties of the Gradient,\MYMACalc3\Part II - Derivatives\DirDerivGrad\PropGrad.html,undefined,\MYMACalc3\Part II - Derivatives\DirDerivGrad\PropGradApps34.html

3 Directional Derivatives and Gradients: Properties of the Gradient

Pythagorean Theorem in \(\mathbb{R}^n\)

Theorem MYMACalc3 Distance Formula in Higher Dimensions (Optional),\MYMACalc3\Part I - Geometry & Vectors\Coords\nDDistance.html

3 Coordinate Systems: Distance Formula in Higher Dimensions (Optional)

Pythagorean Theorem

Theorem MYMACalc3 Distance Formula in 2D,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DDistance.html

3 Coordinate Systems: Distance Formula in 2D

quadrants

Definition MYMACalc3 2D Rectangular Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DRectCoord.html

3 Coordinate Systems: 2D Rectangular Coordinates

quadratic curves

Definition MYMACalc3 undefined,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\CrvR2Quad1.html

3 Curves and Surfaces: undefined

quadratic surfaces

Definition MYMACalc3 undefined,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3Quad1.html

3 Curves and Surfaces: undefined

quadratic

Definition MYMACalc2 What is a Differential Equation?,\MYMACalc2\Part III - Differential Equations\DEIVP\Def.html

2 Differential Equations and Initial Value Problems: What is a Differential Equation?

quadric surfaces

Definition MYMACalc3 undefined,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\SurfR3Quad1.html

3 Curves and Surfaces: undefined

quadric curves

Definition MYMACalc3 undefined,\MYMACalc3\Part I - Geometry & Vectors\CurveSurface\CrvR2Quad1.html

3 Curves and Surfaces: undefined

quotient

Definition MYMACalc2 General Decompositions,\MYMACalc2\Part I - Techniques of Integration\ParFrac\Decomp.html

2 Partial Fractions: General Decompositions

\(r\)-curve

Definition MYMACalc3 2D Polar Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DPolarCoord.html,3D Cylindrical Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\3DCylCoord.html

3 Coordinate Systems: 2D Polar Coordinates

radius

Definition MYMACalc3 2D Polar Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DPolarCoord.html

3 Coordinate Systems: 2D Polar Coordinates

Radius of Convergence Theorem

Theorem MYMACalc2 Radius of Convergence,\MYMACalc2\Part IV - Sequences & Series\PowSer\Radius.html

2 Power Series: Radius of Convergence

radius of convergence

Definition MYMACalc2 Radius of Convergence,\MYMACalc2\Part IV - Sequences & Series\PowSer\Radius.html

2 Power Series: Radius of Convergence

radius of revolution

Definition MYMACalc2 Area of a Surface of Revolution,\MYMACalc2\Part II - Applications of Integration\ArcSurf\SurfRev.html

2 Arc Length and Surface Area: Area of a Surface of Revolution

radius of curvature

Definition MYMACalc3 Curvature,\MYMACalc3\Part I - Geometry & Vectors\CurveProps\Curvature.html

3 Properties of Curves: Curvature

radius

Definition MYMACalc2 Polar Coordinate System,\MYMACalc2\Part II - Applications of Integration\Polar\Def.html

2 Polar Coordinates: Polar Coordinate System

range

Definition MYMACalc3 Domain and Image,\MYMACalc3\Part I - Geometry & Vectors\Functions\DomainImage.html

3 Functions of Several Variables: Domain and Image

ratio of successive terms

Definition MYMACalc2 Geometric Series - Finite,\MYMACalc2\Part IV - Sequences & Series\Ser\GeomFin.html,Geometric Series - Infinite,\MYMACalc2\Part IV - Sequences & Series\Ser\GeomInf.html

2 Series: Geometric Series - Finite

rectangular graph of an equation

Definition MYMACalc3 2D Polar Plots,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DPolarPlot.html

3 Coordinate Systems: 2D Polar Plots

rectangular graph of an equation

Definition MYMACalc2 Graphs of Polar Equations,\MYMACalc2\Part II - Applications of Integration\Polar\Graph.html

2 Polar Coordinates: Graphs of Polar Equations

rectangular equation

Definition MYMACalc3 Polar Equations,\MYMACalc3\Part I - Geometry & Vectors\Coords\2DPolarEq.html

3 Polar Coordinates: Polar Equations

rectangular equation

Definition MYMACalc2 Polar Equations,\MYMACalc2\Part II - Applications of Integration\Polar\PolarEq.html

2 Polar Coordinates: Polar Equations

Rectangular Coordinate System

3 Coordinate Systems: 2D Rectangular Coordinates

rectangular differential of area

Definition MYMACalc3 Polar Coordinates - Grid Cell,\MYMACalc3\Part III - Integrals\CurvInt\Polar-Grid.html

3 Multiple Integrals in Curvilinear Coordinates: Polar Coordinates - Grid Cell

recurrence

Definition MYMACalc2 Recursively Defined Sequences,\MYMACalc2\Part IV - Sequences & Series\Seq\Recur.html

2 Sequences: Recursively Defined Sequences

recursion

Definition MYMACalc2 Recursively Defined Sequences,\MYMACalc2\Part IV - Sequences & Series\Seq\Recur.html

2 Sequences: Recursively Defined Sequences

region of convergence

Definition MYMACalc2 Sequences and Series of Functions,\MYMACalc2\Part IV - Sequences & Series\PowSer\SeqSerFns.html

2 Power Series: Sequences and Series of Functions

related absolute series

Definition MYMACalc2 The Absolute Convergence Test,\MYMACalc2\Part IV - Sequences & Series\SerGen\Abs.html,The Absolute Convergence Test - Proof,\MYMACalc2\Part IV - Sequences & Series\SerGen\AbsPf.html,Overview,\MYMACalc2\Part IV - Sequences & Series\SerGen\Overview.html

2 Convergence of General Series: The Absolute Convergence Test

relation

Definition MYMACalc2 Recursively Defined Sequences,\MYMACalc2\Part IV - Sequences & Series\Seq\Recur.html

2 Sequences: Recursively Defined Sequences

relationship equation

Definition MYMACalc3 Related Rates,\MYMACalc3\Part II - Derivatives\Chain\RelRates.html

3 Chain Rule: Related Rates

relative minimum

3 Functions of Several Variables: Functions of \(1\) Variable

relative maximum

3 Functions of Several Variables: Functions of \(1\) Variable

remainder

Definition MYMACalc2 General Decompositions,\MYMACalc2\Part I - Techniques of Integration\ParFrac\Decomp.html

2 Partial Fractions: General Decompositions

restriction of the function \(f\) to the curve \(\vec r(t)\).

Definition MYMACalc3 Derivative Along a Curve and the Gradient,\MYMACalc3\Part II - Derivatives\DirDerivGrad\DerCurve.html

3 Directional Derivatives and Gradients: Derivative Along a Curve and the Gradient

restriction of the function to the curve

Definition MYMACalc3 Line Integrals of Scalars,\MYMACalc3\Part I - Geometry & Vectors\LineInt\ScalarInt.html

3 Line Integrals: Line Integrals of Scalars

\(\rho\)-curve

Definition MYMACalc3 3D Spherical Coordinates,\MYMACalc3\Part I - Geometry & Vectors\Coords\3DSphCoord.html

3 Coordinate Systems: 3D Spherical Coordinates

Riemann sum

2 Riemann Sums: Riemann Sums and Areas

Riemann sum

Definition MYMACalc1 Riemann Sums and Areas,\MYMACalc1\Part V - Integrals\RiemSum\Def.html,Riemann Sums and Integrals,\MYMACalc1\Part V - Integrals\RiemSum\Def2.html

1 Riemann Sums: Riemann Sums and Areas

Riemann sum

Definition MYMACalc3 Riemann Sum Definition of Single Integrals (Review),\MYMACalc3\Part III - Integrals\RiemInt\1DRiem.html

3 Multiple Integrals as Riemann Sums: Riemann Sum Definition of Single Integrals (Review)

Riemann sum

Definition MYMACalc3 Riemann Sum Definition of Double Integrals,\MYMACalc3\Part III - Integrals\RiemInt\2DRiem.html,Double Integrals over a Rectangle,\MYMACalc3\Part III - Integrals\RiemInt\2DRect.html,Triple Integrals over a Rectangular Box,\MYMACalc3\Part III - Integrals\RiemInt\3DRect.html,Riemann Sum Definition of Triple Integrals,\MYMACalc3\Part III - Integrals\RiemInt\3DRiem.html