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.
Table of Contents
What is a Boundary Problem?
Classification of Partial Differential Equations
Types of Boundary Conditions and the Collocation Method
Differential Equations as Models for Nature
BOUNDARY PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS
Linear Differential Equations
Solving Linear Differential Equations
Differential Equations of Physics and Engineering
Boundary Value Problems and Eigenvalues
Boundary Value Problems as Initial Value Problems
Nonlinear Ordinary Differential Equations
Solutions of Nonlinear Differential Equations
PARTIAL DIFFERENTIAL EQUATIONS
Coordinate Systems and Separability
Methods to Reduce Partial to Ordinary Differential Equations
The Method of Characteristics
Nonlinear Partial Differential Equations
BOUNDARY PROBLEMS WITH ONE CLOSED BOUNDARY
Laplace and Poisson Equations
Conformal Mapping in Two and Three Dimensions
d'Alembert Wave Equation and String Vibrations
Helmholtz Equation and Membrane Vibrations
Rods and the Plate Equation
BOUNDARY PROBLEMS WITH TWO CLOSED BOUNDARIES
Holes in the Domain. Two Boundaries Belonging to Different Coordinate Systems
Corners in the Boundary
NONLINEAR BOUNDARY PROBLEMS
Some Definitions and Examples
Moving and Free Boundaries
Waves of Large Amplitudes. Solitons
The Rupture of an Embankment-Type Water Dam
Gas Flow with Combustion
Cap, Ferdinand F.
"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 codes…and 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