Mathematical Methods in Physics and Engineering with Mathematica
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BeschreibungMathematical Methods in Physics and Engineering with Mathematica provides a reference for practicing engineers, mathematicians, and scientists confronted by difficult problems in ordinary and differential equations and boundary value problems. The author demonstrates how to solve such problems using the software package Mathematica (4.x). The book includes a number of new special solution methods, such as the Lie series method, boundary point collocation methods, and techniques for boundary problems with a hole in the domain, some typical inseparable boundary problems, and problems with very arbitrary forms of the boundary. Mathematica and FORTRAN codes will be available for download from the Internet.
InhaltsverzeichnisINTRODUCTION 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
Pressestimmen"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
Untertitel: 'Chapman & Hall/CRC Applied Mat'. Second. Sprache: Englisch.
Verlag: CRC PR INC
Erscheinungsdatum: Mai 2003
Seitenanzahl: 352 Seiten