Multivariable Calculus

Advanced Calculus using Mathematica: Notebook Edition, by Keith Stroyan, is a complete text on calculus of several variables written in Mathematica Notebooks and described on this site.  It is available as a free Mathematica add-on: Download Add-On (Install Mathematica first).

Many organizations have a site license for Mathematica. Click to find out if you have access.

Click for an overview of the eText or for mathematical themes.

Since the eText is comprised of free-standing Notebooks, there are many ways to use the materials including as a reference to topics often omitted from elementary texts. Click for some suggested uses.

Calculus with Infinitesimals

In 1960 Abraham Robinson showed how to make Leibniz’ approach to calculus rigorous in the sense of modern mathematics.  (He called the theory “non-standard analysis” after a technical name in logic.)  There is a brief course on infinitesimals on this site.

Calculus: The Language of Change

Calculus can be viewed as a language that describes changing quantities.  This is important in mathematics, but also can give us insights to some problems beyond mathematics. Here's my favorite first question in a beginning calculus course: Why did we eradicate polio by vaccination, but not measles?