Div, Grad, Curl, and All That: An Informal Text on Vector Calculus

by Schey,H. M

• ISBN13: 9780393925166
• ISBN10: 0393925161
• Edition: 4th
• Format: Paperback
• Copyright: 2004-12-01
• Publisher: W. W. Norton & Company
• More Book Details

Summary

The Fourth Edition has been carefully revised and now includes updated notations and seven new example exercises.

Table of Contents

Preface to the Fourth Edition	ix
Introduction, Vector Functions, and Electrostatics	1	(10)
Introduction	1	(1)
Vector Functions	2	(3)
Electrostatics	5	(3)
Problems	8	(3)
Surface Integrals and the Divergence	11	(52)
Gauss' Law	11	(1)
The Unit Normal Vector	12	(5)
Definition of Surface Integrals	17	(4)
Evaluating Surface Integrals	21	(10)
Flux	31	(2)
Using Gauss' Law to Find the Field	33	(4)
The Divergence	37	(5)
The Divergence in Cylindrical and Spherical Coordinates	42	(2)
The Del Notation	44	(1)
The Divergence Theorem	45	(4)
Two Simple Applications of the Divergence Theorem	49	(3)
Problems	52	(11)
Line Integrals and the Curl	63	(52)
Work and Line Integrals	63	(3)
Line Integrals Involving Vector Functions	66	(5)
Path Independence	71	(4)
The Curl	75	(7)
The Curl in Cylindrical and Spherical Coordinates	82	(4)
The Meaning of the Curl	86	(5)
Differential Form of the Circulation Law	91	(2)
Stokes' Theorem	93	(6)
An Application of Stokes' Theorem	99	(2)
Stokes' Theorem and Simply Connected Regions	101	(2)
Path Independence and the Curl	103	(1)
Problems	104	(11)
The Gradient	115	(41)
Line Integrals and the Gradient	115	(6)
Finding the Electrostatic Field	121	(3)
Using Laplace's Equation	124	(7)
Directional Derivatives and the Gradient	131	(6)
Geometric Significance of the Gradient	137	(4)
The Gradient in Cylindrical and Spherical Coordinates	141	(3)
Problems	144	(12)
Solutions to Problems	156	(5)
Index	161