Advanced Calculus using Mathematica is a complete text on multivariable calculus that looks like an on-screen math book except that readers can move figures to see them from different positions.  It also links to interactive animations to illustrate things like “zooming in” to see “local linearity.”  Most of the day-to-day work in our courses is traditional paper and pencil work, but the movable figures and links to interactive graphics and animations enhance conceptual understanding and visualization making multivariable calculus accessible at a second semester level.  This allows us to teach important topics that are encountered in physics and engineering courses that are usually taken before the traditional "calc 3."

The text is organized around several mathematical themes that simplify learning the material. By emphasizing the classification of graphs as either explicit, implicit, or parametric, we can treat tangency in a unified way.  Using vectors to help students learn to translate between geometry and algebra, an important basic skill, builds in developing many important concepts.  Local linearity is emphasized in all its cases including integration formulas and flows.

In addition to traditional style exercises, the eText has sections on computing with Mathematica.  The beginning computations are organized like the steps in paper and pencil computations to help improve understanding of that process, but then can be applied to more difficult examples and produce surface and contour graphs and animations that would be difficult "by hand."  These basic computing lessons are extended in "eExams." The progression is: learn the paper and pencil computation, implement it in Mathematica with graphics, and test the concept with an extension.

Some higher dimensional problems are done with Mathematica where the calculus idea is clear, but things like higher dimensional eigenvalues or 6 dimensional constrained critical points are conceptually clear, but difficult to compute by hand.

A few topics often omitted in traditional courses are treated with Mathematica.  For example, linearization of the pendulum is treated several ways.  Click to see descriptions of other novel topics.

We used the text in a second semester calculus course and a more advanced vector calculus course.  Click for some suggested uses.