Mathematical Methods in Physics and Engineering with Mathematica
| Date: 06 May 2011, 19:53
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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.
Review
It is a whirlwind review of mathematical methods used to solve linear and nonlinear boundary-value problems. The best aspect of this book is its immersion in Mathematica, which is treated as a full partner in presenting the material. A list of codesand an appendix that lists all of the Mathematica commands used in the text are nice touches. It will appeal to those who are looking for new perspectives, especially with Mathematica, on familiar topics that they learned elsewhere. It could also be used as a supplementary text in a course which uses an older, standard textbook.
-SIAM Review, Dean Duffy, Annapolis, Maryland
This book is a good example of how to explain and how to use the Mathematica functions and add-on packages for solving various physical and engineering problems from the simplest to the most difficult ones. It is a new type of book, which provides an accessible guide for doing computer aided mathematics.
-Zentralblatt MATH 1044
Contents
1. Introduction
1.1 What is a boundary problem?
1.2 Classification of partial differential equations
1.3 Types of boundary conditions and the collocation method
1.4 Differential equations as models for nature
2 Boundary problems of ordinary differential equations
2.1 Linear differential equations
2.2 Solving linear differential equations
2.3 Differential equations of physics and engineering
2.4 Boundary value problems and eigenvalues
2.5 Boundary value problems as initial value problems
2.6 Nonlinear ordinary differential equations
2.7 Solutions of nonlinear differential equations
3. Partial differential equations
3.1 Coordinate systems and separability
3.2 Methods to reduce partial to ordinary differential equations
3.3 The method of characteristics
3.4 Nonlinear partial differential equations
4 Boundary problems with one closed boundary
4.1 LAPLACE and POISSON equations
4.2 Conformal mapping in two and three dimensions
4.3 D'ALEMBERT wave equation and string vibrations
4.4 HELMHOLTZ equation and membrane vibrations
4.5 Rods and the plate equation
4.6 Approximation methods
4.7 Variational calculus
4.8 Collocation methods
5. Boundary problems with two closed boundaries
5.1 Inseparable problems
5.2 Holes in the domain. Two boundaries belonging to different coordinate systems.
5.3 Corners in the boundary
6. Nonlinear boundary problems
6.1 Some definitions and examples
6.2 Moving and free boundaries
6.3 Waves of large amplitudes. Solitons
6.4 The rupture of an embankment-type water dam
6.5 Gas flow with combustion
References
Appendix
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