Vector Analysis for Mathematicians, Scientists and Engineers (eBook)

The Commonwealth and International Library: Physics Division

S. Simons (Autor)

W. Ashhurst (Herausgeber)

eBook Download: PDF

2014 | 2. Auflage
200 Seiten
Elsevier Science (Verlag)
978-1-4831-6021-4 (ISBN)

Infos

Vector Analysis for Mathematicians, Scientists and Engineers, Second Edition, provides an understanding of the methods of vector algebra and calculus to the extent that the student will readily follow those works which make use of them, and further, will be able to employ them himself in his own branch of science. New concepts and methods introduced are illustrated by examples drawn from fields with which the student is familiar, and a large number of both worked and unworked exercises are provided. The book begins with an introduction to vectors, covering their representation, addition, geometrical applications, and components. Separate chapters discuss the products of vectors; the products of three or four vectors; the differentiation of vectors; gradient, divergence, and curl; line, surface, and volume integrals; theorems of vector integration; and orthogonal curvilinear coordinates. The final chapter presents an application of vector analysis. Answers to odd-numbered exercises are provided as the end of the book.

Inhalt

Front Cover 1
Vector Analysis for Mathematicians, Scientists and Engineers 4
Copyright Page 5
Table of Contents 6
Preface to the First Edition 8
Preface to the Second Edition 8
Chapter 1. Introduction to Vectors 10
1.1 What is a vector? 10
1.2 Representation of vectors 11
1.3 Addition and subtraction of vectors 12
1.4 Simple geometrical applications 15
1.5 Components of a vector 20
Chapter 2. Products of Vectors 26
2.1 The scalar product 26
2.2 The vector product 32
2.3 Applications of scalar and vector products 38
Chapter 3. Products of Three or Four Vectors 45
3.1 The scalar triple product 45
3.2 The vector triple product 48
3.3 Products of four vectors 49
Chapter 4. Differentiation of Vectors 53
4.1 The derivative of a vector 53
4.2 Differentiation of sums and products 55
4.3 Components of a derivative 58
4.4 Applications to mechanics 62
4.5 Integration of vectors 68
4.6 Partial differentiation 71
Chapter 5. Gradient, Divergence and Curl 74
5.1 Vector and scalar fields 74
5.2 The gradient operator 78
5.3 The divergence operator 85
5.4 The curl operator 88
5.5 Grad, div and curl of products 90
5.6 Double application of . operator 96
5.7 Invariance properties of . 102
Chapter 6. Line, Surface and Volume Integrals 110
6.1 Line integrals 110
6.2 Surface integrals 117
6.3 Volume integrals 128
Chapter 7. Theorems of Vector Integration 133
7.1 Conservative vector fields 133
7.2 The divergence theorem 136
7.3 Stokes' theorem 145
Chapter 8. Orthogonal Curvilinear Coordinates 153
8.1 Vector components in a general orthogonal coordinate system 153
8.2 Differential operators for orthogonal coordinates 159
Chapter 9. An Application of Vector Analysis— Electrical Theory 167
9.1 Electrostatic field and potential 167
9.2 Gauss' theorem 171
9.3 Poisson's and Laplace's equations 173
9.4 Energy of the electrostatic field 174
9.5 Dipoles 176
9.6 Conductors and insulators 178
9.7 Electric current 180
9.8 Magnetic effects of a current 182
9.9 Magnetic vector potential 183
9.10 Continuous current distributions 184
9.11 Energy of the magnetic field 185
9.12 Electromagnetic induction 188
9.13 The displacement current 189
9.14 Maxwell's equations 190
9.15 The electromagnetic potentials 192
9.16 Electromagnetic waves 193
Answers to Odd-numbered Exercises 196
Index 198

Produkt-Details

• Erscheint lt. Verlag: 15.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Technik
• ISBN-10: 1-4831-6021-1 / 1483160211
• ISBN-13: 978-1-4831-6021-4 / 9781483160214