Mathematical methods in physics and engineering with Mathematica

✍ Scribed by Ferdinand Cap

• Publisher: Chapman & Hall/CRC
• Year: 2003
• Tongue: English
• Leaves: 340
• Series: Chapman & Hall/CRC applied mathematics and nonlinear science series
• Edition: 1
• Category: Library

✦ Synopsis

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

Content: 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. method of characteristics --
3.4. Nonlinear partial differential equations --
4. Boundary problem 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. Solutions --
6.4. rupture of an embankment-type water dam --
6.5. Gas flow with combustion.