Cap Mathematical Methods in Physics and Engineering with Mathematica

Erscheinungsjahr 2003
ISBN: 978-0-203-50260-0
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 352 Seiten

Reihe: Chapman & Hall/CRC Applied Mathematics & Nonlinear Science

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.

Zielgruppe

Applied mathematicians, engineers, physicists; computer and software scientists; and graduate students in those disciplines

Autoren/Hrsg.

Cap, Ferdinand F.

Fachgebiete

• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Mathematik | Informatik EDV | Informatik Business Application Integrierte Softwarepakete
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Naturwissenschaften Physik Physik Allgemein

Inhaltsverzeichnis

INTRODUCTION
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
Approximation Methods
Variational Calculus
Collocation Methods
BOUNDARY PROBLEMS WITH TWO CLOSED BOUNDARIES
Inseparable Problems
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
REFERENCES
APPENDIX
INDEX