Vector Analysis and Cartesian Tensors

✍ Scribed by D. E. Bourne and P. C. Kendall (Auth.)

• Publisher: Elsevier Inc, Academic Press
• Year: 1977
• Tongue: English
• Leaves: 263
• Edition: 2nd
• Category: Library

✦ Synopsis

This is a comprehensive and self-contained text suitable for use by undergraduate mathematics, science and engineering students. Vectors are introduced in terms of cartesian components, making the concepts of gradient, divergent and curl particularly simple. The text is supported by copious examples and progress can be checked by completing the many problems at the end of each section. Answers are provided at the back of the book

✦ Table of Contents

Content:
Front Matter, Page iii
Dedication, Page iv
Copyright, Page iv
PREFACE, Pages v-vi
CHAPTER 1 - RECTANGULAR CARTESIAN COORDINATES AND ROTATION OF AXES, Pages 1-17,17A
CHAPTER 2 - SCALAR AND VECTOR ALGEBRA, Pages 18-48
CHAPTER 3 - VECTOR FUNCTIONS OF A REAL VARIABLE. DIFFERENTIAL GEOMETRY OF CURVES, Pages 49-70
CHAPTER 4 - SCALAR AND VECTOR FIELDS, Pages 72-115,115A,115B
CHAPTER 5 - LINE, SURFACE, AND VOLUME INTEGRALS, Pages 116-158
CHAPTER 6 - INTEGRAL THEOREMS, Pages 159-185
CHAPTER 7 - APPLICATIONS IN POTENTIAL THEORY, Pages 186-203
CHAPTER 8 - CARTESIAN TENSORS, Pages 204-223
CHAPTER 9 - REPRESENTATION THEOREMS FOR ISOTROPIC TENSOR FUNCTIONS, Pages 224-238
APPENDIX 1 - Determinants, Pages 239-240
APPENDIX 2 - The chain rule for Jacobians, Page 241
APPENDIX 3 - Expressions for grad, div, curl, and ∇2 in cylindrical and spherical polar coordinates, Page 242
ANSWERS TO EXERCISES, Pages 243-250
GENERAL INDEX, Pages 251-256