Mathematical Methods in Physics and

More than ever before, complicated mathematical procedures are integral to the success and advancement of technology, engineering, and even industrial production. Knowledge of and experience with these procedures is therefore vital to present and future scientists, engineers and technologists.Mathematical Methods in Physics and Engineering with Mathematica clearly demonstrates how to solve difficult practical problems involving ordinary and partial differential equations and boundary value problems using the software package Mathematica (4.x). Avoiding mathematical theorems and numerical methods-and requiring no prior experience with the software-the author helps readers learn by doing with step-by-step recipes useful in both new and classical applications.Mathematica and FORTRAN codes used in the book's examples and exercises are available for download from the Internet. The author's clear explanation of each Mathematica command along with a wealth of examples and exercises make Mathematical Methods in Physics and Engineering with Mathematica an outstanding choice both as a reference for practical problem solving and as a quick-start guide to using a leading mathematics software package.

Ferdinand F. Cap is Professor Emeritus, Theoretical Physics, University of Innsbruck, Austria.

Introduction	p. 1
What is a boundary problem?	p. 1
Classification of partial differential equations	p. 12
Types of boundary conditions and the collocation method	p. 18
Differential equations as models for nature	p. 22
Boundary problems of ordinary differential equations	p. 27
Linear differential equations	p. 27
Solving linear differential equations	p. 31
Differential equations of physics and engineering	p. 44
Boundary value problems and eigenvalues	p. 51
Boundary value problems as initial value problems	p. 59
Nonlinear ordinary differential equations	p. 68
Solutions of nonlinear differential equations	p. 80
Partial differential equations	p. 91
Coordinate systems and separability	p. 91
Methods to reduce partial to ordinary differential equations	p. 104
The method of characteristics	p. 116
Nonlinear partial differential equations	p. 126
Boundary problems with one closed boundary	p. 137
Laplace and Poisson equations	p. 137
Conformal mapping in two and three dimensions	p. 156
D'Alembert wave equation and string vibrations	p. 168
Helmholtz equation and membrane vibrations	p. 174
Rods and the plate equation	p. 188
Approximation methods	p. 202
Variational calculus	p. 214
Collocation methods	p. 223
Boundary problems with two closed boundaries	p. 241
Inseparable problems	p. 241
Holes in the domain. Two boundaries belonging to different coordinate systems	p. 263
Corners in the boundary	p. 279
Nonlinaer boundary problems	p. 285
Some definitions and examples	p. 285
Moving and free boundaries	p. 288
Waves of large amplitudes. Solitons	p. 295
The rupture of an embankment-type water dam	p. 306
Gas flow with combustion	p. 310
References	p. 313
Appendix	p. 325
Index	p. 334
Table of Contents provided by Rittenhouse. All Rights Reserved.

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Mathematical Methods in Physics and Engineering With Mathematica

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