this book also available online at http://www.math.gatech.edu/~cain/notes/calculus.html, written by George Cain and 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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