Welcome to mecmath.net

This site is the homepage for the free book Vector Calculus, by Michael Corral (Schoolcraft College). If you are looking for the Trigonometry homepage, go here.

You can download the latest version (2009-07-22) of Vector Calculus here: calc3book.pdf
Note: The above file gets updated only with corrections (of typos, errors, etc). No new material gets added, and no material gets removed.

The book is a PDF file, which requires a PDF viewer such as the freely available Adobe Acrobat Reader or noncommercial software (e.g. xpdf, Evince) to view it. The book is distributed under the terms of the GNU Free Documentation License, Version 1.2.

The PDF file above includes color graphics. You can buy a printed, bound, paperback version of the book with grayscale graphics for $11 plus shipping at the book's project page on Lulu.com: http://www.lulu.com/mecmath.
The price covers just the cost of printing (Lulu.com recently increased their base price, which is why the price is now $11 instead of the original $8.93). The grayscale version is also available as a free download at that site.

For those who want to view and/or compile the book's source files, the LaTeX source code is available here: calc3book-1.0-src.tar.gz
You will need a relatively recent LaTeX installation to compile the source code. A build script (calc3book.sh) for Linux/UNIX systems is included for building the PDF file. See the included README file for more instructions.

Java examples: The Java programs and source code for Newton's algorithm (Ch. 2) and the Monte Carlo method (Ch. 3) can be downloaded here: calc3book_java.zip
These are the programs listed in Section 2.6 and Section 3.4 of the book. The source files can be modified easily to solve some of the exercises in those sections.

Book description: This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals.

The book also includes discussion of numerical methods: Newton's method for optimization, and the Monte Carlo method for evaluating multiple integrals. There is a section dealing with applications to probability. Appendices include a proof of the right-hand rule for the cross product, and a short tutorial on using Gnuplot for graphing functions of 2 variables.

There are 420 exercises in the book. Answers to selected exercises are included.

TABLE OF CONTENTS

1. Vectors in Euclidean Space
   • Introduction
   • Vector Algebra
   • Dot Product
   • Cross Product
   • Lines and Planes
   • Surfaces
   • Curvilinear Coordinates
   • Vector-Valued Functions
   • Arc Length
2. Functions of Several Variables
   • Functions of Two or Three Variables
   • Partial Derivatives
   • Tangent Plane to a Surface
   • Directional Derivatives and the Gradient
   • Maxima and Minima
   • Unconstrained Optimization: Numerical Methods
   • Constrained Optimization: Lagrange Multipliers
3. Multiple Integrals
   • Double Integrals
   • Double Integrals Over a General Region
   • Triple Integrals
   • Numerical Approximation of Multiple Integrals
   • Change of Variables in Multiple Integrals
   • Application: Center of Mass
   • Application: Probability and Expected Value
4. Line and Surface Integrals
   • Line Integrals
   • Properties of Line Integrals
   • Green's Theorem
   • Surface Integrals and the Divergence Theorem
   • Stokes' Theorem
   • Gradient, Divergence, Curl and Laplacian

• Bibliography
• Appendix A: Answers and Hints to Selected Exercises
• Appendix B: Proof of the Right-Hand Rule for the Cross Product
• Appendix C: 3D Graphing with Gnuplot
• GNU Free Documentation License
• History
• Index

News

(2009-09-13) The author's new book, Trigonometry, is now available. The homepage is located here: mecmath.net/trig/

(2009-07-22) The prequel to this book, which will be titled Elementary Calculus, is in preparation. It will cover calculus of a single variable. The aim is to have it available by the end of this year or early next year. Another book, on trigonometry, is almost finished and should be available here by the end of August 2009. Both books will be free and released under the GNU Free Documentation License, complete with the LaTeX source code.

(2009-07-22) In Appendix A, the answer to Exercise 5 in Section 2.3 was corrected. Thanks to E. Cavazos for pointing out the error. This is the only change in the new version (2009-07-22) from the previous version (2009-03-29).

(2009-07-10) Prof. Marshall Hampton of the University of Minnesota, Duluth has kindly posted some notes on compiling the LaTeX source code for the book under OS X, which you can read here.