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.


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


20 March 2000