Latest news:

There is now a preliminary version of the 2013 edition in html format.

This is the 2012 edition of the multivariable calculus book; you can still get the 2011 version. I have added a few exercises and made some minor alterations. Also the pagination has changed: the book is now numbered starting at 1 for the cover page; there is no longer a portion numbered with roman numerals. This means the page number corresponds to the actual page in the "whole book" pdf file. There is a new section on numerical integration for chapter 8 (section 6), covering the trapezoid method and Simpson's rule.

Until the 2013 edition I will generally make only minor changes that do not change pagination, such as typos and wrong answers to exercises. I will keep a list of changes in the changelog.

Albert Schueller has provided some webwork assignments for Calculus II and Calculus III , if you are running a WebWork server.

[] You can get a printed copy of the book at frequently has special offers for discounts or free shipping; check the main lulu page before you order.

Other versions of the book:

If you want to print out the text, you should probably download individual chapters; if you want to read the book on a computer screen, the "whole book" is a better choice, as it contains live links that let you easily jump from place to place in the book and to documents and demonstrations on the web. The links "2 up" and "4 up" will give you versions with two or four book pages per printed page.

You can download the source code. (This usually lags the pdf version; email me if it is behind and you want the current source.)

The PDF reader from Adobe might not let you markup these pdf files. There is a nice, free PDF viewer for Windows that will allow you to read them and add highlighting, sticky tabs, etc. It is at

Send comments, suggestions, corrections, and contributions to

Last update: February 1, 2013, 14:14

Table of Contents and Introduction (2 up) (4 up)

Chapter 1: Analytic Geometry (2 up) (4 up)

Chapter 2: The Derivative (2 up) (4 up)

Chapter 3: Rules for Finding Derivatives (2 up) (4 up)

Chapter 4: Transcendental Functions (2 up) (4 up)

Chapter 5: Curve Sketching (2 up) (4 up)

Chapter 6: Applications of the Derivative (2 up) (4 up)

Chapter 7: Integration (2 up) (4 up)

Chapter 8: Techniques of Integration (2 up) (4 up)

Chapter 9: Applications of Integration (2 up) (4 up)

Chapter 10: Polar Coordinates, Parametric Equations (2 up) (4 up)

Chapter 11: Sequences and Series (2 up) (4 up)

Chapter 12: Three Dimensions (2 up) (4 up)

Chapter 13: Vector Functions (2 up) (4 up)

Chapter 14: Partial Differentiation (2 up) (4 up)

Chapter 15: Multiple Integration (2 up) (4 up)

Chapter 16: Vector Calculus (2 up) (4 up)

Chapter 17: Differential Equations (2 up) (4 up)

Appendix A: Answers (2 up) (4 up)

Appendix B: Useful Formulas (2 up) (4 up)

Index (2 up) (4 up)

The Whole Book