Eliezer / Langford / Maxwell Concise Vector Analysis

The Commonwealth and International Library of Science, Technology, Engineering and Liberal Studies: Mathematics Division
1. Auflage 2014
ISBN: 978-1-4831-4193-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 164 Seiten, Web PDF

Concise Vector Analysis is a five-chapter introductory account of the methods and techniques of vector analysis. These methods are indispensable tools in mathematics, physics, and engineering. The book is based on lectures given by the author in the University of Ceylon. The first two chapters deal with vector algebra. These chapters particularly present the addition, representation, and resolution of vectors. The next two chapters examine the various aspects and specificities of vector calculus. The last chapter looks into some standard applications of vector algebra and calculus. This book will prove useful to applied mathematicians, students, and researchers.

Autoren/Hrsg.

Eliezer, C. J.

Langford, W. J.

Maxwell, E. A.

Sneddon, I. N.

Inhaltsverzeichnis

1;Front Cover;1
2;Concise Vector Analysys;4
3;Copyright Page;5
4;Table of Contents;6
5;PREFACE;8
6;Chapter 1. Vectors and Vector Addition;10
6.1;1.1. Vectors;10
6.2;1.2. Representation of vectors;11
6.3;1.3 Vector addition;12
6.4;1.4 - a , O, .a;14
6.5;1.5 Resolution of a vector;16
6.6;1.6 Point dividing AB in the ratio m:n
;19
6.7;1.7 Centroid or mean centre of n points;21
6.8;Exercises I;23
7;Chapter 2. Products of Vectors;25
7.1;2.1 Scalar product;25
7.2;2.2 Vector product;31
7.3;2.3 Triple products;37
7.4;2.4 Mutual moment of two lines;39
7.5;2.5 Positive and negative triads;40
7.6;Exercise IIc
;41
8;Chapter 3. Vector Calculus;47
8.1;3.1 Vector function of a scalar;47
8.2;3.2 Unit tangent vector .;51
8.3;3.3 Functions of a vector;53
8.4;3.4 Map of a field;54
8.5;3.5 Directional derivative;57
8.6;3.6 Gradient vector;59
8.7;Exercises III
;64
9;Chapter 4. Vector Calculus
;67
9.1;4.1 Line integrals;67
9.2;4.2 Line integral of grad ø
;74
9.3;4.3 Surface integrals;80
9.4;4.4 Volume integrals;87
9.5;4.5 Divergence;90
9.6;4.6 Gauss's transformatio;94
9.7;4.7 Curl A;97
9.8;4.8 Stokes' theorem;101
9.9;4.9 The operator .;103
9.10;4.10 The Laplacian operator;105
9.11;4.11 Orthogonal curvilinear coordinates;105
9.12;Exercises 4;107
10;Chapter 5. Some Applications;112
10.1;5.1 Equivalence of force systems;112
10.2;5.2 Poinsot's Central Axis;116
10.3;5.3 Space-curve;122
10.4;5.4 Infinitesimal rotations. Angular velocity;126
10.5;5.5 Angular velocity of a rigid body;128
10.6;5.6 Gauss's theorem;133
10.7;5.7 Gravitational potential;139
10.8;5.8 Equipotential surfaces;149
10.9;5.9 Green's theorems;151
10.10;Exercises 5
;154
11;Index;160