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.

Title page and 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 Five - More Dimensions**

5.1 The space **R ^{n}**

5.2 Functions

**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:R^{n}-› 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

20 March 2000