We provide instructional and supplemental learning materials for various topics in math.

# MYMathApps Calculus 1: Differential Calculus

A Web Based, Interactive, Multimedia Calculus

Doing, Not Just Viewing

Learn Differential Calculus easily with the interactive MYMathApps Calculus 1 online textbook

## Benefits of MYMACalc 1 over Other Texts

• In the PreCalculus chapter on Vectors, there is a graphical proof of the Triangle Inequality.
• In the chapter on Intuitive Limits, the tutorial shows students a graph or a piecewise-defined function and asks them to determine the limits from the left and right and the 2-sided limit and then to decide if the function is continuous from the left or right or both.
• Plots and animations are used in the proofs or justifications of the Intermediate Value, Extreme Value and Mean Value Theorems.
• There is the “standard” animation of the secant lines on a graph rotating into tangent lines, but there is also an animation of secant vectors on a parametric curve rotating into the tangent vector to show why the velocity (the derivative of the position) is actually tangent to the curve.
• Animations demonstrate the Linear Approximation, Newton's Method, Related Rates and Max/Min Problems.
• The convergence of Rieman Sums is demonstrated by the “standard” animation.
• The Fundamental Theorem of Calculus is proved using animated areas.
• A tutorial for Average Value allows students to move a slider to guess the average value before computing it.

## Benefits of an Online Text

Although primarily a standard calculus text, the online format allows for many features which are impossible in a static book:

• There are many animations directly in the pages, some of which can be modified real-time by the student.
• The text is fully hyperlinked. The material is designed to be followed linearly, with frequent side excursions for extra material such as additional examples, background information, proofs or advanced material.
• Most pages in the text cover a single topic followed by an example and an exercise. More exercises appear on a linked exercise page. Hints, answers and full solutions for the exercises toggle in dropdown regions directly below the exercise. Hopefully, students try the problems before they click on the answer or solution button. The solution is not right there in front of them as in a paper book.
• When there is an obvious way to check an answer, the check appears in a light green region at the end of the an example's solution, or in a separate drop down region after an exercise. For example:
After solving an equation, one should check it by substituting the solution back into the equation.
After finding an antiderivative, one should check by differentiating.
After finding the center of mass of an object, one should check that it is inside (the convex hull of) the object.
• Sometimes there is a comment or remark about an exercise, that the author would like to make which might have given away the answer if visible in the page. In that case there is an additional button at the end of the exercise to drop down the remark. For example:
The integral you just computed gives the area of a semi-circle. So you could have known the answer in advance.
• Many books give formulas without proof. MYMACalc proves every formula. Derivations and proofs are directly in the text when they are essential to understanding, but are frequently hidden in a drop-down region when they are not essential, so they do not obstruct the flow of the material but are still easily accessible to interested students. There are many more proofs than most textbooks.
• There are exercise pages for each chapter and the exercises are grouped by section of the chapter. Each group is hyperlinked back to the appropriate pages, to facilitate those students who like to start on the exercises and only read the chapter when they need help doing the exercises.
• There are links to the Maplets for Calculus (M4C) directly in the text. These drill the students on specific topics acting like a “Tutor without the Tutor”. Since the M4C are displayed in Java, they cannot be viewed on most mobile devices. Consequently, they are gradually being converted into browser-based tutorials which either are directly embedded in the text or appear on separate tutorial pages.
• MYMACalc works in any browser on any device, except for the Maplets for Calculus (M4C) (because they are Java based).