Mathematical Models in Applied Mechanics

Name: Mathematical Models in Applied Mechanics
Price: 69.73 USD
Availability: InStock
ISBN: 9780198535331

ISBN-10: 0198535333

ISBN-13: 9780198535331

Edition: 1986

Authors: A. B. Tayler

List price: $45.00

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This book outlines the philosophy and techniques needed for the application of mathematics to industrial and scientific problems. Taking a practice-oriented approach, the author includes twenty-one problems, all of which illustrate the power of differential equations in industrial applications. The problems presented touch upon a wide range of situations, including smoke dispersion from a high chimney, the hot rolling of steel, resonance in a gear box, submarine detection, and the shape of laser meltpools. Tayler pays particular attention to the formulation of these problems and has carefully ordered them to illustrate the coherent development of partial differential equations.

Book details

List price: $45.00
Copyright year: 1986
Publisher: Oxford University Press, Incorporated
Publication date: 3/20/1986
Binding: Hardcover
Pages: 200
Size: 5.75" wide x 8.75" long x 0.82" tall
Weight: 0.990

Problem Formulation
Introduction	p. 1
Normalization of the problem	p. 2
Perturbation procedures	p. 5
Furnace reaction analysis	p. 6
Analytical methods for ordinary differential equations	p. 9
Classical analogies	p. 21
Exercises	p. 31
Wave Motion
Transverse waves on a stretched string	p. 37
Pantograph dynamics I, periodic motion	p. 40
Second-order hyperbolic equations and weak solutions	p. 45
Pantograph dynamics II	p. 50
Linear hyperbolic systems in two independent variables	p. 53
A regenerative heat exchanger	p. 55
Multiple reflections and use of transforms	p. 59
Short circuit in a transformer	p. 61
Wave motion with two or more space variables	p. 65
Submarine detection	p. 68
Waveguides and dispersion	p. 74
Coal seam exploration	p. 78
Quasi-linear systems	p. 81
Flow of granular material in a hopper	p. 83
Exercises	p. 89
Elliptic Problems
Potential theory	p. 95
Current flow between two plates joined by spigots	p. 97
Variational methods and variational inequalities	p. 102
Electrochemical painting	p. 105
Free-boundary problems	p. 107
Percolation in a sand dune	p. 113
Application of complex variable methods	p. 116
Wave reflection from a visco-elastic raft	p. 122
Quasi-static continuum models	p. 128
The hot rolling of steel	p. 133
Exercises	p. 140
Diffusion
The diffusion equation	p. 145
Somke dispersion from a high chimney	p. 150
Stefan problems	p. 154
Welding of two steel plates	p. 159
Weak solutions	p. 164
Dendritic growth	p. 171
Diffusion and convection	p. 175
The shape of laser melt-pools	p. 181
Non-linear diffusion	p. 186
The spreading of an oil film	p. 193
Exercises	p. 197
Asymptotic Methods for Non-linear Problems
Non-linear ordinary differential equations	p. 203
Resonance in a gearbox	p. 212
Thin layers and lubrication theory	p. 219
The impregnation of paper by a resin	p. 225
Boundary layers	p. 233
Injection moulding	p. 244
Far-field solutions	p. 249
Seismic detection	p. 257
Exercises	p. 263
Bibliography	p. 269
Index	p. 273
Table of Contents provided by Syndetics. All Rights Reserved.