The Calculus of Functions of Several Variables

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A companion single-variable calculus text, Difference Equations to Differential Equations, is available here.

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Chapter 1: Geometry of Rⁿ

Introduction to Rⁿ

Angles and the dot product

The cross product

Lines, planes, and hyperplanes

Linear and affine functions

Operations with matrices

Chapter 2: Functions from R to Rⁿ

Curves

Best affine approximations

Motion along a curve

Chapter 3: Functions from Rⁿ to R

Geometry, limits, and continuity

Directional derivatives and the gradient

Best affine approximations

Second-order approximations

Extreme values

Definite integrals

Change of variables in integrals

Chapter 4: Functions from R^m to Rⁿ

Geometry, limits, and continuity

Best affine approximations

Line integrals

Green's theorem

Copyright © 1999, 2001 by Dan Sloughter.

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Last modified: Tuesday 18 March 2008 9:18 EDT

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