Table of Contents

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• Geometry & Vectors
  1. Coordinate Systems Available as Sample
     1. Rectangular Coordinates - 2D, 3D and nD   1   2   3
        1. 2D Rectangular Coordinates
        2. 3D Rectangular Coordinates
        3. Rectangular Coordinates in Higher Dimensions (Optional)
     2. Distance Formula - 2D, 3D and nD   1   2   3
        1. Distance Formula in 2D
        2. Distance Formula in 3D
        3. Distance Formula in Higher Dimensions (Optional)
     3. Polar Coordinates - 2D   1   2   3   4
        1. 2D Polar Coordinates
        2. Converting between Rectangular and Polar
        3. Polar Equations
        4. Polar Plots
     4. Cylindrical and Spherical Coordinates - 3D and nD   1   2   3
        1. 3D Cylindrical Coordinates
        2. 3D Spherical Coordinates
        3. Cylindrical and Spherical Coordinates in Higher Dimensions (Optional)
     5. Exercises   (HW)   1
        1. Exercises
  2. Functions of Several Variables
     1. Functions   1   2
        1. Formulas
        2. Domain and Image
     2. Graphs   1   2
        1. Graphs of Functions
        2. Graphs of Equations
     3. Level Sets and Contour Plots   1   2   3
        1. Functions of \(1\) Variable
        2. Functions of \(2\) Variables
           1. Topological Map of Mt. St. Helen
        3. Functions of \(3\) Variables
     4. Maxima, Minima and Saddle Points   1   2   3
        1. Functions of \(1\) Variable
        2. Functions of \(2\) Variables
        3. Identifying Maxima, Minima and Saddle Points
     5. Exercises   (HW)   1
        1. Exercises
  3. Vectors
     1. Definition, Magnitude and Direction   1   2   3   4
        1. Vectors as Arrows
        2. The Vector Between Two Points - Displacement
        3. Magnitude
        4. Direction
     2. Free vs. Located vs. Field   1   2   3
        1. Free vs. Located
        2. Located vs. Field
        3. Plots of Vector Fields
     3. Vector Addition   1   2   3
        1. Algebraic Definition
        2. Geometric Construction
        3. Properties
           1. Triangle Inequality - Proof
     4. Scalar Multiplication   1   2   3
        1. Algebraic Definition
        2. Geometric Construction
        3. Properties
     5. Linear Combinations and \(ijk\) Notation   1   2
        1. Linear Combinations
        2. \(ijk\) Notation
     6. Applications   1   2
        1. Balancing Forces
        2. Orienteering
     7. Exercises   (HW)   1
        1. Exercises
  4. Dot Product
     1. Definitions   1   2   3
        1. Algebraic Definition
        2. Properties
        3. Geometric Formula
     2. Angles   1
        1. Angles
     3. Projections   1   2
        1. Vector Projections
        2. Scalar Projections
     4. Applications   1
        1. Work
     5. Exercises   (HW)   1
        1. Exercises
  5. Cross Product Available as Sample
     1. Determinants   1   2   3
        1. Method of Diagonals
        2. Expansion by Minors on a Row or Column
        3. Properties of Determinants
     2. Cross Product and Triple Product   1   2   3   4   5
        1. Algebraic Definition of Cross Products
        2. Algebraic Definition of Triple Products
        3. Properties of Cross Products
        4. Right Hand Rule
        5. Geometric Interpretation of Cross Products
     3. Area   1
        1. Area
     4. Volume   1   2
        1. Volume
        2. Triple Product: Geometric Interpretation
     5. Applications   1
        1. Balancing Torques
     6. Exercises   (HW)   1
        1. Exercises
  6. Lines and Planes
     1. Lines - Parametric Equations   1   2
        1. Derivation
        2. Reparametrizing a Line
     2. Lines - Non-Parametric Equations   1   2   3
        1. Derivation
        2. Special Formulas in \(\mathbb{R}^2\)
        3. Alternate Derivation of the Normal Equation in \(\mathbb{R}^2\)
     3. Distance From a Point to a Line   1   2
        1. Distance in \(\mathbb{R}^3\)
        2. Distance in \(\mathbb{R}^2\)
     4. Parallel, Intersecting, and Skew Lines   1   2
        1. Parallel and Intersecting Lines in \(\mathbb{R}^2\)
        2. Parallel, Intersecting and Skew Lines in \(\mathbb{R}^3\)
     5. Planes - Parametric Equations   1   2
        1. Derivation
           1. More Examples
        2. Reparametrizing a Plane
     6. Planes - Non-Parametric Equations   1   2   3
        1. Derivation
           1. More Examples
        2. Alternate Derivation of the Normal Equation in \(\mathbb{R}^3\)
        3. Perpendicular Lines and Planes
     7. Distance From a Point to a Plane   1
        1. Distance From a Point to a Plane
     8. Parallel and Intersecting Planes   1
        1. Parallel and Intersecting Planes
     9. Parallel and Intersecting Lines and Planes   1
        1. Parallel and Intersecting Lines and Planes
     10. Review of Lines and Planes   1
         1. Review of Lines and Planes
     11. Exercises   (HW)   1
         1. Exercises
  7. Curves and Surfaces
     1. Preview of Curves and Surfaces   1
        1. Preview of Curves & Surfaces
     2. Curves in \(\mathbb{R}^{2}\)   1   2   3
        1. Parametric Curves in \(\mathbb{R}^{2}\)
        2. Quadratic Curves - Part \(1\)
        3. Quadratic Curves - Part \(2\)
     3. Curves in \(\mathbb{R}^{3}\)   1
        1. Parametric Curves in \(\mathbb{R}^{3}\)
     4. Surfaces in \(\mathbb{R}^{3}\)   1   2   3
        1. Parametric Surfaces in \(\mathbb{R}^{3}\)
        2. Quadratic Surfaces - Part \(1\)
        3. Quadratic Surfaces - Part \(2\)
     5. Exercises   (HW)   1
        1. Exercises
  8. Properties of Curves Available as Sample
     1. Vector Functions, Position, Velocity and Plots   1   2
        1. Vector Functions: Position and Plots
        2. Vector Functions: Velocity and Force
     2. Limits and Derivatives of Vector Functions   1   2
        1. Limits of Vector Functions
        2. Derivatives of Vector Functions
     3. Velocity, Acceleration, and Jerk   1
        1. Velocity, Acceleration, and Jerk
     4. Arc Length, Arc Length Parameter, and Speed   1   2   3
        1. Arc Length of a Curve
        2. Arc Length Parameter
        3. Speed
     5. Tangent, Normal, and Binormal Vectors   1   2
        1. Definitions
        2. Computational Formulas
     6. Curvature and Torsion   1   2
        1. Curvature
        2. Torsion
           1. Torsion Formula Proof
     7. Tangential and Normal Acceleration   1
        1. Tangential and Normal Acceleration
     8. Summary & Examples of Curve Computations   1   2
        1. Summary of Curve Computations
        2. Examples of Curve Computations
           1. Circle
           2. Helix
           3. Cubic
           4. Cubic Spiral Helix
     9. Frenet Frames (Optional)   1
        1. Frenet Frames & Derivatives of TNB (Optional)
     10. Tutorial on Properties of Curves   1
         1. Tutorial on Properties of Curves
     11. Exercises   (HW)   1
         1. Exercises
  9. Line Integrals Available as Sample
     1. Arc Length   1
        1. Arc Length
     2. Line Integrals of Scalars   1
        1. Line Integrals of Scalars
     3. Applications of Scalar Line Integrals   1   2   3
        1. Mass, Center of Mass & Centroid
        2. Average Value
        3. Probability & Expected Value
     4. Line Integrals of Vectors   1
        1. Line Integrals of Vectors
     5. Applications of Vector Line Integrals   1   2
        1. Work
        2. Flow and Circulation
     6. Normal Line Integrals in \(\mathbb{R}^2\) (Optional)   1
        1. Normal Line Integrals in \(\mathbb{R}^2\) (Optional)
     7. Applications of Normal Line Integrals (Optional)   1
        1. Expansion
     8. Exercises   (HW)   1
        1. Exercises
• Derivatives
  10. Limits and Continuity
      1. Intuitive Limits and Continuity for Functions of \(1\) Variable (Review)   1   2
         1. When Limits Exist
         2. When Limits Do Not Exist
      2. Intuitive Limits for Functions of \(2\) Variables   1   2   3   4
         1. When Limits Exist
         2. When Limits Do Not Exist
         3. When Limits May or May Not Exist
         4. Computing Limits using Polar Coordinates
      3. Limit Laws   1
         1. Limit Laws
      4. Continuity   1
         1. Continuity
      5. Intuitive Limits and Continuity with \(n\) Variables (Optional)   1
         1. Intuitive Limits and Continuity with \(n\) Variables (Optional)
      6. Precise Limits for Functions of \(1\) Variable (Optional, Review)   1
         1. Precise Limits for Functions of \(1\) Variable (Optional, Review)
      7. Precise Limits for Functions of \(2\) Variables (Optional)   1
         1. Precise Limits for Functions of \(2\) Variables (Optional)
      8. Exercises   (HW)   1
         1. Exercises
  11. Partial Derivatives and Tangent Planes Available as Sample
      1. Computation of Partial Derivatives   1
         1. Computation of Partial Derivatives
      2. Algebraic Definition of Partial Derivatives   1
         1. Algebraic Definition of Partial Derivatives
      3. Geometric Interpretation of Partial Derivatives   1
         1. Geometric Interpretation of Partial Derivatives
      4. Tangent Plane to the Graph of a Function   1   2
         1. Geometric Derivation
         2. Algebraic Formula
            1. Tangent Line to the Graph of a Function
            2. Comparison of Tangent Line and Tangent Plane Derivations
      5. More Variables   1
         1. More Variables
      6. Tutorials   1
         1. Trace and Tangent Plane Tutorial
      7. Exercises   (HW)   1
         1. Exercises
  12. Linear Approximation
      1. Differentials and Linear Approximation with \(1\) Variable   1   2
         1. Changes and Differentials with \(1\) Variable
         2. Linear Approximation with \(1\) Variable
      2. Differentials and Linear Approximation with \(2\) Variables   1   2
         1. Changes and Differentials with \(2\) Variables
         2. Linear Approximation with \(2\) Variables
      3. Differentials and Linear Approximation with \(3\) Variables   1   2
         1. Changes and Differentials with \(3\) Variables
         2. Linear Approximation with \(3\) Variables
      4. Exercises   (HW)   1
         1. Exercises
  13. Chain Rule
      1. Composition of Functions   1
         1. Composition of Functions
      2. Chain Rule   1   2   3   4
         1. Chain Rule with \(1\) Intermediate Variable
         2. Chain Rule with \(2\) Intermediate Variables
         3. Chain Rule with More Intermediate Variables
         4. Chain Rule with More Independent Variables
      3. Nested Chain Rule   1
         1. Nested Chain Rule
      4. Implicit Differentiation   1   2
         1. Implicit Differentiation with \(1\) Variable
         2. Implicit Partial Differentiation
      5. Related Rates   1
         1. Related Rates
      6. Exercises   (HW)   1
         1. Exercises
  14. Directional Derivatives and Gradients Available as Sample
      1. Derivative along a Curve and the Gradient   1
         1. Derivative along a Curve and the Gradient
      2. Derivative along a Vector   1
         1. Derivative along a Vector
      3. Directional Derivatives   1   2
         1. Directional Derivatives
         2. Applications of Directional Derivatives
      4. Properties of the Gradient   1   2   3
         1. Properties of the Gradient
         2. Applications of Gradient Properties 1 & 2
         3. Applications of Gradient Properties 3 & 4
      5. Tangent and Normal, Lines and Planes to Level Sets   1   2   3
         1. Tangent Lines to Level Curves in \(\mathbb R^2\)
         2. Tangent Planes to Level Surfaces in \(\mathbb R^3\)
         3. Normal Lines to Level Sets
      6. Exercises   (HW)   1
         1. Exercises
  15. Higher Derivatives
      1. Higher Derivatives   1   2
         1. Definition
         2. Geometrical Interpretation (Optional)
      2. Clairaut's Theorem   1
         1. Clairaut's Theorem
      3. The Hessian   1
         1. The Hessian
      4. Taylor Series and Polynomials   1   2
         1. Taylor Series and Polynomials for \(1\) Variable
         2. Taylor Series and Polynomials for \(2\) Variables
            1. Derivation of Taylor Series for \(2\) Variables
      5. Exercises   (HW)   1
         1. Exercises
  16. Max-Min Problems Available as Sample
      1. Local Minima, Local Maxima and Saddle Points   1   2   3   4
         1. Functions of \(1\) Variable
         2. Functions of \(2\) Variables
         3. Second Derivative Test - Examples
         4. Second Derivative Test with More Variables (Optional)
      2. Constrained Max-Min Problems   1   2   3
         1. Eliminate a Variable Method
         2. Lagrange Multiplier Method
         3. Parametrization Method (Optional)
      3. Global Max-Min Problems   1
         1. Global Max-Min Problems
      4. Multiple Constraint Problems (Optional)   1
         1. Multiple Constraint Problems (Optional)
      5. Exercises   (HW)   1
         1. Exercises
  17. Divergence, Curl and Potentials Available as Sample
      1. The Del Operator   1
         1. The Del Operator
      2. The Divergence Operator   1   2
         1. Algebraic Definition of Divergence
         2. Geometric Interpretation of the Divergence
      3. The Curl Operator   1   2
         1. Algebraic Definition of Curl
         2. Geometric Interpretation of the Curl
      4. Differential Identities   1   2
         1. First Order Differential Identities
         2. Second Order Differential Operators and Identities
            1. The Divergence of a Gradient (\(\vec\nabla\cdot\vec\nabla f\)) - The Laplacian
            2. The Curl of a Gradient (\(\vec\nabla\times\vec\nabla f\))
            3. The Divergence of a Curl (\(\vec\nabla\cdot\vec\nabla\times\vec F\))
            4. The Curl of a Curl (\(\vec\nabla\times\vec\nabla\times\vec F\))
      5. Generalizing Antiderivatives   1
         1. Generalizing Antiderivatives
      6. Scalar Potentials   1   2
         1. Finding Scalar Potentials
         2. Non-Existence of a Scalar Potential
      7. Vector Potentials   1   2
         1. Finding Vector Potentials
         2. Non-Existence of a Vector Potential
      8. Exercises   (HW)   1
         1. Exercises
• Integrals
  18. Iterated Integrals
      1. Computing Iterated Integrals   1   2
         1. Computing Iterated Integrals with Constant Limits
         2. Computing Iterated Integrals with Functional Limits
      2. Factoring Iterated Integrals   1
         1. Factoring Iterated Integrals
      3. Exercises   (HW)   1
         1. Exercises
  19. Multiple Integrals as Riemann Sums
      1. Riemann Sum Definition of Single Integrals (Review)   1
         1. Riemann Sum Definition of Single Integrals (Review)
      2. Riemann Sum Definition of Double Integrals   1   2
         1. Definition
         2. Double Integrals over a Rectangle
      3. Riemann Sum Definition of Triple Integrals   1   2
         1. Definition
         2. Triple Integrals over a Rectangular Box
      4. Properties of Integrals   1   2   3   4
         1. Length, Area, and Volume
         2. Sums and Constant Multiples
         3. Inequalities and Bounds on the Integrals
         4. Split the Region
      5. Exercises   (HW)   1
         1. Exercises
  20. Multiple Integrals in Rectangular Coordinates
      1. Double Integrals over a Non-Rectangular Region   1   2   3
         1. Type \(x\) and Type \(y\) Regions
            1. Derivations
         2. Double Integrals over a Region which is both Type \(x\) and Type \(y\)
         3. Reversing the Order of Integration
            1. Summary
      2. Applications of Double Integrals   1   2   3   4   5   6
         1. Volume
         2. Area
         3. Average Value of a Function
         4. Centroid of a Region
         5. Mass
         6. Center of Mass
      3. Triple Integrals over a Non-Rectangular Region   1   2   3
         1. Region Types
         2. Examples
         3. Changing the Order of Integration
      4. Applications of Triple Integrals   1   2   3   4   5   6
         1. 4-Volume (Optional)
         2. Volume
         3. Average Value of a Function
         4. Centroid of a Region
         5. Mass
         6. Center of Mass
      5. Exercises   (HW)   1
         1. Exercises
  21. Multiple Integrals in Curvilinear Coordinates Available as Sample
      1. Integrating in Polar Coordinates   1   2   3   4   5
         1. Grid Cells
         2. Integral over a Polar Rectangle
            1. Derivation
         3. Integral over a Non-Rectangular Polar Region
            1. Derivation
         4. Applications
         5. Converting & Mixing, Rectangular & Polar Coordinates
      2. Integrating in Cylindrical Coordinates   1   2   3   4
         1. Grid Cells
         2. Integral over a Cylindrical Region
         3. Applications
         4. Converting & Mixing, Rectangular & Cylindrical Coordinates
      3. Integrating in Spherical Coordinates   1   2   3   4
         1. Grid Cells
         2. Integral over a Spherical Region
         3. Applications
         4. Converting & Mixing, Rectangular & Spherical Coordinates
      4. Integrating in 2D Curvilinear Coordinates   1   2   3   4   5   6
         1. Grid Cells
         2. Grid Cell Area
         3. The Jacobian
         4. Ellipse Example
         5. Diamond Shaped Examples
         6. Applications
      5. Integrating in 3D Curvilinear Coordinates   1   2   3   4   5
         1. Grid Cells
         2. Grid Cell Volume
         3. The Jacobian
         4. Ellipsoid Example
         5. Applications
      6. Exercises   (HW)   1
         1. Exercises
  22. Parametric Surfaces and Surface Integrals Available as Sample
      1. Introduction to Parametric Surfaces   1
         1. Position and Plots
      2. Tangent and Normal Vectors   1   2   3
         1. Coordinate Curves
         2. Tangent Vectors
         3. Normal Vector
      3. Scalar Surface Integrals   1   2
         1. Grid Cells and Scalar Surface Area Differential
         2. Formulas
      4. Applications of Scalar Surface Integrals   1   2   3   4   5
         1. Surface Area
         2. Average Value on a Surface
         3. Centroid
         4. Mass
         5. Center of Mass
      5. Vector Surface Integrals   1   2   3
         1. Vector Surface Area Differential
         2. Orientations
         3. Alternate Notations
      6. Applications of Vector Surface Integrals   1
         1. Flux and Expansion
      7. Exercises   (HW)   1
         1. Exercises
• Theorems
  23. Preview of Theorems, Review of Integrals   (Read the first 2 pages. The rest is optional.)
      1. The Vector Calculus Theorems   1   2
         1. Statements
         2. Properties
      2. Geometric Domains and their Orientations (Optional)   1   2   3   4
         1. Domains & Orientations in \(\mathbb{R}\)
         2. Domains & Orientations in \(\mathbb{R}^{2}\)
         3. Domains & Orientations in \(\mathbb{R}^{3}\)
         4. Domains & Orientations in \(\mathbb{R}^{n}\)
      3. Review of Integrals (Optional)   1   2   3   4
         1. Integrals in \(\mathbb{R}\)
         2. Integrals in \(\mathbb{R}^{2}\)
            1. Region Integrals
            2. Scalar Line Integrals
            3. Vector Line Integrals
            4. Normal Vector Line Integrals
         3. Integrals in \(\mathbb{R}^{3}\)
            1. Region Integrals
            2. Scalar Line Integrals
            3. Vector Line Integrals
            4. Scalar Surface Integrals
            5. Vector Surface Integrals
         4. Integrals in \(\mathbb{R}^{n}\)
      4. Boundaries and Their Orientations (Optional)   1   2   3   4
         1. Boundaries and Orientations in \(\mathbb{R}\)
         2. Boundaries and Orientations in \(\mathbb{R}^{2}\)
         3. Boundaries and Orientations in \(\mathbb{R}^{3}\)
         4. Boundaries and Orientations in \(\mathbb{R}^{n}\)
      5. Exercises   (HW)   1
         1. Exercises
  24. Fundamental Theorem of Calculus for Curves
      1. The Theorem   1
         1. The Theorem
      2. Which Line Integrals Can be Done Using the FTCC?   1
         1. Which Line Integrals Can be Done Using the FTCC?
      3. Verification   1
         1. Verification
      4. Proof   1
         1. Proof
      5. Applications   1   2
         1. Path Independence
         2. Work
            1. Newtonian Gravitational Force
            2. Gravitational Force near the Earth
            3. Coulomb Electrostatic Force
      6. Exercises   (HW)   1
         1. Exercises
  25. Green's Theorem
      1. The Theorem   1   2
         1. Statement
         2. The Theorem for Regions with Holes
      2. Verification   1
         1. Verification
      3. Proof   1
         1. Proof
            1. Rectangles
            2. Regions of Type \(y\)
      4. Alternate Notations   1   2
         1. 2D Stokes' Theorem
         2. 2D Gauss' Theorem
      5. Applications   1   2   3
         1. Converting Line Integrals to Region Integrals
         2. Converting Region Integrals to Line Integrals
         3. Total Rotation and Circulation
      6. Exercises   (HW)   1
         1. Exercises
  26. Stokes' Theorem (The Curl Theorem) Available as Sample
      1. The Theorem   1   2   3
         1. Statement
         2. Surfaces whose Boundaries have Several Curves
         3. Surfaces with No Boundary
      2. Verification   1
         1. Verification
      3. Proof   1
         1. Proof
      4. Applications   1   2   3   4   5   6
         1. Converting Line Integrals to Surface Integrals
         2. Converting Surface Integrals to Line Integrals
         3. Path Independence
         4. Surface Independence
         5. Circulation and Vorticity of a Fluid
         6. Ampere's Law
      5. Exercises   (HW)   1
         1. Exercises
  27. Gauss' Theorem (The Divergence Theorem) Available as Sample
      1. The Theorem   1   2
         1. Statement
         2. Solids with Holes
      2. Verification   1
         1. Verification
      3. Proof   1
         1. Proof
      4. Applications   1   2   3   4   5
         1. Converting Surface Integrals to Volume Integrals
         2. Converting Volume Integrals to Surface Integrals
         3. Surface Independence
         4. Fluid Flow
         5. Gauss' Law
      5. Exercises   (HW)   1
         1. Exercises
  28. Interpretation of Divergence and Curl
      1. Interpretation of Divergence   1
         1. Interpretation of Divergence
      2. Interpretation of Curl   1
         1. Interpretation of Curl
      3. Exercises   (HW)   1
         1. Exercises
  29. Sample Exams
      1. Math 221 Fall 2021   1
         1. Math 221 Fall 2021
      2. Math 251 Fall 2020   1
         1. Math 251 Fall 2020
      3. Math 221 Fall 2019   1
         1. Math 221 Fall 2019
      4. Math 221H Fall 2019   1
         1. Math 221H Fall 2019
      5. Math 251 Fall 2018   1
         1. Math 251 Fall 2018
      6. Math 251 Fall 2017   1
         1. Math 251 Fall 2017
      7. Math 251 Fall 2016   1
         1. Math 251 Fall 2016
      8. Math 253H Fall 2016   1
         1. Math 253H Fall 2016
      9. Math 251 Fall 2015   1
         1. Math 251 Fall 2015
      10. Math 251 Fall 2014   1
          1. Math 251 Fall 2014
      11. Math 253H Fall 2014   1
          1. Math 253H Fall 2014
      12. Math 251 Spring 2013   1
          1. Math 251 Spring 2013
      13. Math 221 Fall 2012   1
          1. Math 221 Fall 2012
      14. Math 251 Fall 2012   1
          1. Math 251 Fall 2012
      15. Math 253H Fall 2012   1
          1. Math 253H Fall 2012
      16. Math 221 Spring 2011   1
          1. Math 221 Spring 2011
      17. Math 251 Spring 2011   1
          1. Math 251 Spring 2011
      18. Math 251 Spring 2010   1
          1. Math 251 Spring 2010
      19. Math 221 Fall 2009   1
          1. Math 221 Fall 2009
      20. Math 253 Fall 2009   1
          1. Math 253 Fall 2009
      21. Math 253 Spring 2009   1
          1. Math 253 Spring 2009
      22. Math 253 Fall 2008   1
          1. Math 253 Fall 2008
      23. Math 251 Spring 2008   1
          1. Math 251 Spring 2008
      24. Math 253 Spring 2008   1
          1. Math 253 Spring 2008
      25. Math 251 Spring 2007   1
          1. Math 251 Spring 2007
      26. Math 253 Spring 2007   1
          1. Math 253 Spring 2007
      27. Math 251 Fall 2006   1
          1. Math 251 Fall 2006
      28. Math 253H Fall 2006   1
          1. Math 253H Fall 2006
      29. Math 251 Spring 2006   1
          1. Math 251 Spring 2006
      30. Math 251 Fall 2005   1
          1. Math 251 Fall 2005
      31. Math 253 Spring 2004   1
          1. Math 253 Spring 2004
      32. Math 253 Fall 2003   1
          1. Math 253 Fall 2003
      33. Math 253 Spring 2003   1
          1. Math 253 Spring 2003
      34. Math 253H Fall 2002   1
          1. Math 253H Fall 2002
      35. Math 253H Fall 1999   1
          1. Math 253H Fall 1999
      36. Math 253H Spring 1999   1
          1. Math 253H Spring 1999
      37. Math 253 Fall 1998   1
          1. Math 253 Fall 1998
      38. Math 253 Spring 1998   1
          1. Math 253 Spring 1998
      39. Math 221 Spring 1997   1
          1. Math 221 Spring 1997
      40. Math 253 Spring 1997   1
          1. Math 253 Spring 1997
      41. Math 253 Fall 1996   1
          1. Math 253 Fall 1996
      42. Math 221 Fall 1991   1
          1. Math 221 Fall 1991
      43. Exercises   (HW)   1
          1. Exercises