Multivariable Calculus George Cain & James Herod © Copyright 1996, 1997 by George Cain and James Herod. All rights reserved.



This is a textbook for a course in multivariable calculus. It has been used for the past few years here at Georgia Tech. The notes are available as Adobe Acrobat documents. If you do not have an Adobe Acrobat Reader, you may down-load a copy, free of charge, from Adobe.



Table of Contents

Chapter One - Euclidean Three Space

1.1 Introduction

1.2 Coordinates in Three-Space

1.3 Some Geometry

1.4 Some More Geometry--Level Sets

Chapter Two - Vectors--Algebra and Geometry

2.1 Vectors

2.2 Scalar Product

2.3 Vector Product



Chapter Three - Vector Functions

3.1 Relations and Functions

3.2 Vector Functions

3.3 Limits and Continuity



Chapter Four - Derivatives

4.1 Derivatives

4.2 Geometry of Space Curves--Curvature

4.3 Geometry of Space Curves--Torsion

4.4 Motion



Chapter Six - Linear Functions and Matrices

6.1 Matrices

6.2 Matrix Algebra



Chapter Seven - Continuity, Derivatives, and All That

7.1 Limits and Continuity

7.2 Derivatives

7.3 The Chain Rule



Chapter Eight - f:Rn- R

8.1 Introduction

8.2 The Directional Derivative

8.3 Surface Normals

8.4 Maxima and Minima

8.5 Least Squares

8.6 More Maxima and Minima

8.7 Even More Maxima and Minima

Chapter Nine - The Taylor Polynomial

9.1 Introduction

9.2 The Taylor Polynomial

9.3 Error

Supplementary material for Taylor polynomial in several variables.

Chapter Ten - Sequences, Series, and All That

10.1 Introduction

10.2 Sequences

10.3 Series

10.4 More Series

10.5 Even More Series

10.6 A Final Remark

Chapter Eleven - Taylor Series

11.1 Power Series

11.2 Limit of a Power Series

11.3 Taylor Series

Chapter Twelve - Integration

12.1 Introduction

12.2 Two Dimensions



Chapter Thirteen - More Integration

13.1 Some Applications

13.2 Polar Coordinates

13.3 Three Dimensions



Chapter Fourteen - One Dimension Again

14.1 Scalar Line Integrals

14.2 Vector Line Integrals

14.3 Path Independence



Chapter Fifteen - Surfaces Revisited

15.1 Vector Description of Surfaces

15.2 Integration

Chapter Sixteen - Integrating Vector Functions

16.1 Introduction

16.2 Flux

Chapter Seventeen - Gauss and Green

17.1 Gauss's Theorem

17.2 Green's Theorem

17.3 A Pleasing Application

Chapter Eighteen - Stokes

18.1 Stokes's Theorem

18.2 Path Independence Revisited

Chapter Ninteen - Some Physics

19.1 Fluid Mechanics

19.2 Electrostatics

