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

Description

This new fourth edition of the acclaimed and bestselling Div, Grad, Curl, and All That has been carefully revised and now includes updated notations and seven new example exercises. Since the publication of the First Edition over thirty years ago, Div, Grad, Curl, and All That has been widely renowned for its clear and concise coverage of vector calculus, helping science and engineering students gain a thorough understanding of gradient, curl, and Laplacian operators without required knowledge of advanced mathematics. 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