Author(s): H. M. Schey
Edition: 3
Publisher: W. W. Norton & Company
Year: 1997
Language: English
Pages: 0
Preface 9
Chapter I Introduction, Vector Functions, and Electrostatics 11
Introduction 11
Vector Functions 12
Electrostatics 15
Problems 19
Chapter II Surface Integrals and the Divergence 21
Gauss' Law 21
The Unit Normal Vector 22
Definition of Surface Integrals 27
Evaluating Surface Integrals 31
Flux 39
Using Gauss' Law to Find the Field 42
The Divergence 46
The Divergence in Cylindrical and SphericalCoordinates 51
The Del Notation 53
The Divergence Theorem 54
Two Simple Applications of the Divergence Theorem 59
Problems 62
Chapter III Line Integrals and the Curl 73
Work and Line Integrals 73
Line Integrals Involving Vector Functions 76
Path Independence 80
The Curl 85
The Curl in Cylindrical and Spherical Coordinates 92
The Meaning of the Curl 95
Differential Form of the Circulation Law 100
Stokes' Theorem 102
An Application of Stokes' Theorem 108
Stokes' Theorem and Simply Connected Regions 110
Path Independence and the Curl 111
Problems 112
Chapter IV The Gradient 124
Line Integrals and the Gradient 124
Finding the Electrostatic Field 131
Using Laplace's Equation 133
Directional Derivatives and the Gradient 140
Geometric Significance of the Gradient 147
The Gradient in Cylindrical and Spherical Coordinates 150
Problems 153
Solutions to Problems 166
Bibliography 170
Index 172
