Simons / Ashhurst Vector Analysis for Mathematicians, Scientists and Engineers

The Commonwealth and International Library: Physics Division
2. Auflage 2014
ISBN: 978-1-4831-6021-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 200 Seiten, Web PDF

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.

Autoren/Hrsg.

Simons, S.

Ashhurst, W.

Inhaltsverzeichnis

1;Front Cover;1
2;Vector Analysis for Mathematicians, Scientists and Engineers;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface to the First Edition;8
6;Preface to the Second Edition;8
7;Chapter 1. Introduction to Vectors;10
7.1;1.1 What is a vector?;10
7.2;1.2 Representation of vectors;11
7.3;1.3 Addition and subtraction of vectors;12
7.4;1.4 Simple geometrical applications;15
7.5;1.5 Components of a vector;20
8;Chapter 2. Products of Vectors;26
8.1;2.1 The scalar product;26
8.2;2.2 The vector product;32
8.3;2.3 Applications of scalar and vector products;38
9;Chapter 3. Products of Three or Four Vectors;45
9.1;3.1 The scalar triple product;45
9.2;3.2 The vector triple product;48
9.3;3.3 Products of four vectors;49
10;Chapter 4. Differentiation of Vectors;53
10.1;4.1 The derivative of a vector;53
10.2;4.2 Differentiation of sums and products;55
10.3;4.3 Components of a derivative;58
10.4;4.4 Applications to mechanics;62
10.5;4.5 Integration of vectors;68
10.6;4.6 Partial differentiation;71
11;Chapter 5. Gradient, Divergence and Curl;74
11.1;5.1 Vector and scalar fields;74
11.2;5.2 The gradient operator;78
11.3;5.3 The divergence operator;85
11.4;5.4 The curl operator;88
11.5;5.5 Grad, div and curl of products;90
11.6;5.6 Double application of . operator;96
11.7;5.7 Invariance properties of .;102
12;Chapter 6. Line, Surface and Volume Integrals;110
12.1;6.1 Line integrals;110
12.2;6.2 Surface integrals;117
12.3;6.3 Volume integrals;128
13;Chapter 7. Theorems of Vector Integration;133
13.1;7.1 Conservative vector fields;133
13.2;7.2 The divergence theorem;136
13.3;7.3 Stokes' theorem;145
14;Chapter 8. Orthogonal Curvilinear Coordinates;153
14.1;8.1 Vector components in a general orthogonal coordinate system;153
14.2;8.2 Differential operators for orthogonal coordinates;159
15;Chapter 9. An Application of Vector Analysis— Electrical Theory;167
15.1;9.1 Electrostatic field and potential;167
15.2;9.2 Gauss' theorem;171
15.3;9.3 Poisson's and Laplace's equations;173
15.4;9.4 Energy of the electrostatic field;174
15.5;9.5 Dipoles;176
15.6;9.6 Conductors and insulators;178
15.7;9.7 Electric current;180
15.8;9.8 Magnetic effects of a current;182
15.9;9.9 Magnetic vector potential;183
15.10;9.10 Continuous current distributions;184
15.11;9.11 Energy of the magnetic field;185
15.12;9.12 Electromagnetic induction;188
15.13;9.13 The displacement current;189
15.14;9.14 Maxwell's equations;190
15.15;9.15 The electromagnetic potentials;192
15.16;9.16 Electromagnetic waves;193
16;Answers to Odd-numbered Exercises;196
17;Index;198