Div, Grad, Curl, and All That: An Informal Text on Vector Calculus [4 ed.] 9780393925166
This new fourth edition of the acclaimed and bestselling Div, Grad, Curl, and All That has been carefully revised and no
379 58 22MB
English Pages 176 [178] Year 2004
Table of contents :
Contents
Preface
1 Introduction, Vector Functions, and Electrostatics
Introduction
Vector Functions
Electrostatics
Problems
2 Surface Integrals and the Divergence
Gauss's Law
The Unit Normal Vector
Definitinos of Surface Integrals
Evaluating Surface Integrals
Flux
Using Gauss's Law to Find the Field
The Divengence
The Divergence in Cylindrical and Spherical Coordinates
The Del Notation
The Divergence Theorem
Two Simple Applications of the Divengence Theorem
Problems
3 Line Integrals and the Curl
Work and Line Integrals
Line Integrals Involving Vector Functions
Path Independence
The Curl
The Curl in Cylindrical and Spherical Coordinates
The Meaning of the Curl
Differential Form of the Circulation Law
Stoke's Theorem
An Application of Stoke's Theorem
Stoke's Theorem and Simply Connected Regions
Path Independence and the Curl
Problems
4 The Gradient
Line Integrals and the Gradient
Finding the Electrostatic Field
Using Laplace's Equation
Directional Derivatives and the Gradient
Geometric SIgnificance of the Gradient
The Gradient in Cylindrical and Spherical Coordinates
Problems
Solutions
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Index
Reference
Contents
Preface
1 Introduction, Vector Functions, and Electrostatics
Introduction
Vector Functions
Electrostatics
Problems
2 Surface Integrals and the Divergence
Gauss's Law
The Unit Normal Vector
Definitinos of Surface Integrals
Evaluating Surface Integrals
Flux
Using Gauss's Law to Find the Field
The Divengence
The Divergence in Cylindrical and Spherical Coordinates
The Del Notation
The Divergence Theorem
Two Simple Applications of the Divengence Theorem
Problems
3 Line Integrals and the Curl
Work and Line Integrals
Line Integrals Involving Vector Functions
Path Independence
The Curl
The Curl in Cylindrical and Spherical Coordinates
The Meaning of the Curl
Differential Form of the Circulation Law
Stoke's Theorem
An Application of Stoke's Theorem
Stoke's Theorem and Simply Connected Regions
Path Independence and the Curl
Problems
4 The Gradient
Line Integrals and the Gradient
Finding the Electrostatic Field
Using Laplace's Equation
Directional Derivatives and the Gradient
Geometric SIgnificance of the Gradient
The Gradient in Cylindrical and Spherical Coordinates
Problems
Solutions
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Index
Reference
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