Multivariable Calculus

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,

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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