This is the pre-alpha of the multivariable calculus site. The new site is under development for use in all browsers, touchpads, and smartphones. It will be released in Beta by January 2014.

The pre-alpha of the site can be accessed at http://math.etsu.edu/multicalc/prealpha .

WORKS ONLY WITH SOME VERSIONS OF INTERNET EXPLORER AND GOOGLE CHROME. DOES NOT WORK IN FIREFOX!!

# Multivariable Calculus Online

(supported in part by National Science Foundation grant DUE-9950600)

 1.1 Vectors in 2 and 3 dimensions 1.2 The Dot Product 1.3 The Cross Product 1.5 Parametric Equations 1.6 Velocity and Acceleration 1.8 Components of Acceleration

 2.1 Functions of 2 Variables 2.2 Limits and Continuity 2.3 Partial Derivatives 2.4 Partial Differential Equations 2.5 Linearization and the Hessian 2.6 The Chain Rule 2.8 Optimization 2.9 Lagrange Multipliers

 3.1 Coordinate Transformations 3.2 Polar Coordinates 3.3 The Jacobian 3.4 Surfaces 3.5 Curvilinear Coordinates 3.7 DIFF GEOM: Curves on Surfaces

 4.1 Iterated Integrals 4.2 Double Integrals 4.3 Applications of the Double Integral 4.5 Double Integrals in Polar Coordinates 4.6 Triple Integrals

 5.1 Vector Fields 5.2 Line Integrals 5.3 Potentials of Conservative Fields 5.4 Green's Theorem 5.5 Surface Integrals 5.7 Stoke's Theorem

 C.1. Uniform Circular Motion C.2. Conservation Laws C.3. Kepler's Laws C.4. Satellites and Planets C.5. Electric and Magnetic Fields C.6. Maxwell's Equations C.7. Special Relativity C.8. General Relativity - An Overview

 Individual Sections Maple Worksheets Online Tools The Entire Course

 Optimized for 1024 X 768 resolution Developed for Windows IE 6.0 or 7.0 Patch for Netscape and Mozilla MacIntosh Users MATHML Version -- Coming Soon Mathematica Notebooks -- Coming Soon

### © Copyright 2001 by Jeff Knisley,  Dept. of Math., East Tennessee State University.  Free for individual use only.  No portion of this textbook may be altered or sold.

Multivariable Calculus Online is adapted from the textbook Calculus: A Modern Approach by Kevin Shirley and Jeff Knisley.

Development of Multivariable Calculus Online was funded in part by National Science Foundation grant DUE-9950600.

Many of the applets and images were prepared with Javaview, an excellent web-based visualization tool which is free for download and can be used with Maple 6 through 9.

Additional applets were prepared with LiveGraphics3d, an excellent complement to Mathematica featuring parameterized graphics.

Sections written in LaTeX2e and converted to html with TTHGold.  Final editing was performed with Microsoft Frontpage and Eversoft 1stPage2000.

A special thanks to my wife, Debra, for all her support, suggestions, guidance, and encouragement.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the
views of the National Science Foundation.

 Javaview Eversoft 1stPage2000.