文档介绍：CLASSICAL ELECTRODYNAMICS
for Undergraduates
Professor John W. Norbury
Physics Department
University of Wisconsin-Milwaukee
. Box 413
Milwaukee, WI 53201
1997
Contents
1 MATRICES 5
Einstein Summation Convention ................ 5
Coupled Equations and Matrices ................ 6
Determinants and Inverse .................... 8
Solution of Coupled Equations ................. 11
Summary ............................. 11
Problems ............................. 13
Answers .............................. 14
Solutions ............................. 15
2 VECTORS 19
Basis Vectors ........................... 19
Scalar Product .......................... 20
Vector Product .......................... 22
Triple and Mixed Products ................... 25
Div, Grad and Curl (di
erential calculus for vectors) ..... 26
Integrals of Div, Grad and Curl ................. 31
Fundamental Theorem of Gradients .......... 32
Gauss’ theorem (Fundamental theorem of Divergence) 34
Stokes’ theorem (Fundamental theorem of curl) .... 35
Potential Theory ......................... 36
Curvilinear Coordinates ..................... 37
Plane Cartesian (Rectangular) Coordinates ...... 37
Three dimensional Cartesian Coordinates ....... 38
Plane (2-dimensional) Polar Coordinates ....... 38
Spherical (3-dimensional) Polar Coordinates ..... 40
Cylindrical (3-dimensional) Polar Coordinates .... 41
Div, Grad and Curl in Curvilinear Coordinates .... 43
1
2 CONTENTS
Summary ............................. 43
Problems ............................. 44
Answers .............................. 46
Solutions ............................. 47
Figure captions for chapter 2 .................. 51
3 MAXWELL’S EQUATIONS 53
Maxwell’s equations in di
erential form ............ 54
Maxwell’s equations in