Multivariable Calculus
George Cain & James Herod
Title page and Table of Contents

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 Rn
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: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

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http://www.math.gatech.edu/~cain/notes/calculus.html