by

## David Guichard and friends

### Department of Mathematics Whitman College

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License. To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-sa/4.0/ or send a letter to Creative Commons, 543 Howard Street, 5th Floor, San Francisco, California, 94105, USA. If you distribute this work or a derivative, include the history of the document.

This text was initially written by David Guichard. The single variable material in chapters 1–9 is a modification and expansion of notes written by Neal Koblitz at the University of Washington, who generously gave permission to use, modify, and distribute his work. New material has been added, and old material has been modified, so some portions now bear little resemblance to the original.

The book includes some exercises and examples from Elementary Calculus: An Approach Using Infinitesimals, by H. Jerome Keisler, available at http://www.math.wisc.edu/~keisler/calc.html under a Creative Commons license. In addition, the chapter on differential equations is largely derived from the corresponding chapter in Keisler's book. Some exercises are from the OpenStax Calculus books, available free at https://openstax.org/subjects/math. Albert Schueller, Barry Balof, and Mike Wills have contributed additional material.

This HTML version was produced by software written by David Farmer, Albert Schueller, and David Guichard. It is generated from the $\rm\TeX$ source; the output of $\rm \TeX$ should be treated as the definitive version; it is available as a pdf file at https://www.whitman.edu/mathematics/multivariable.

This HTML version of the book includes some interactive content. Most of this content is of two types: 3D figures and Sage worksheet cells. 3D figures can typically be rotated (by dragging with the mouse) to see them from different angles, and can be zoomed with a mouse wheel; an example is the pyramid in figure 9.3.1.

Sage is a Computer Algebra System, similar to Mathematica and Maple, that can do many types of calculation and graphing. The book has some Sage cells that allow you to use Sage to do various computations, and generally are prefilled with an example; most of these are at the beginning of exercise sections. An example is the exercise section for section 16.6.

You can find help with Sage in various places on the web, including the final chapter of this book, https://doc.sagemath.org/html/en/tutorial/tour_algebra.html and https://doc.sagemath.org/html/en/prep/Calculus.html.