Dover Books on Mathematics

By: D E Rutherford

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Paperback | 11 August 2004

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135 Pages

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21.59 x 13.34 x 0.64

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Designed to familiarize undergraduates with the methods of vector algebra and vector calculus, this text offers both a clear view of the abstract theory as well as a concise survey of the theory's applications to various branches of pure and applied mathematics. A chapter on differential geometry introduces readers to the study of this subject by the methods of vector algebra. The next section explores the many aspects of the theory of mechanics adaptable to the use of vectors, and a full discussion of the vector operator ""nabla"" proceeds to a treatment of potential theory and Laplace's equation. This includes applications to the theories of gravitation, hydrodynamics, and electricity. A brief chapter on four-dimensional vectors concludes the text.

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Non-Fiction Mathematics Calculus & Mathematical Analysis

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Non-Fiction Mathematics Calculus & Mathematical Analysis

Preface	p. v
Vector Algebra	p. 1
Addition of Vectors	p. 1
Products of Vectors	p. 5
Differentiation of Vectors	p. 10
Examples	p. 10
Points, Lines and Planes	p. 11
Applications to Geometry	p. 12
Examples	p. 15
Differential Geometry	p. 16
Osculating Plane	p. 16
Frenet's Formulae	p. 19
Curvature	p. 20
Intrinsic Equations	p. 21
Canonical Equations	p. 23
The Helix	p. 23
Examples	p. 25
Fundamental Quadratic Forms	p. 26
Lines of Curvature	p. 29
Euler's Theorem	p. 32
Asymptotic Lines	p. 33
The Paraboloid of Revolution	p. 34
Examples	p. 35
Applications to Mechanics	p. 37
Forces and Moments	p. 37
Systems of Particles	p. 42
Rigid Bodies	p. 45
Angular Velocities	p. 46
Moving Axes	p. 47
Moments and Products of Inertia	p. 50
Virtual Work	p. 55
Energy	p. 56
Examples	p. 58
The Vector Operator "[down triangle, open]"	p. 60
Gradient, Curl and Divergence	p. 60
Identities involving "[down triangle, open]"	p. 68
Orthogonal Curvilinear Coordinates	p. 69
Stokes's Theorem and Gauss's Theorem	p. 73
Green's Theorem	p. 75
Examples	p. 77
Potential Theory	p. 78
Scalar Potential	p. 78
Field Tubes	p. 80
Sources, Sinks and Dipoles	p. 81
Equations of Poisson and Laplace	p. 84
Surface Distributions	p. 85
Potentials of Given Distributions	p. 87
Equipotential Surfaces	p. 93
Vector Potential	p. 95
Conductors and Dielectrics	p. 97
Examples	p. 100
Hydrodynamics	p. 102
Stream and Vortex Lines	p. 102
Differentiation following the Motion	p. 103
Equation of Continuity	p. 104
Equations of Motion	p. 105
Vorticity	p. 107
Examples	p. 110
Laplace's Equation	p. 111
Conditions satisfied by the Potential	p. 111
Determination of the Distribution	p. 114
The Electrostatic Problem	p. 116
Solutions of Laplace's Equation	p. 117
Examples	p. 122
Four-Dimensional Vectors	p. 123
Four-Dimensional Vector Calculus	p. 123
The Space Time World	p. 126
Electro-Magnetic Field Equations	p. 126
Momentum World-Vector	p. 128
Conservation of Energy	p. 130
Bibliography	p. 132
Index	p. 133
Table of Contents provided by Ingram. All Rights Reserved.

Dover Books on Mathematics

At a Glance

Paperback

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How to return your order

Defective items

You Can Find This Book In

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