Scientific computing with mathematica : mathematical problems for ordinary differential equations
著者
書誌事項
Scientific computing with mathematica : mathematical problems for ordinary differential equations
（Modeling and simulation in science, engineering & technology）
Birkhäuser, 2001
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注記
Includes bibliographical references (p. 267-268) and index
内容説明・目次
内容説明
Many interesting behaviors of real physical, biological, economical,
and chemical systems can be described by ordinary differential
equations (ODEs).
Scientific Computing with Mathematica for Ordinary Differential
Equations
provides a general framework useful for the applications, on the
conceptual aspects of the theory of ODEs, as well as a sophisticated
use of Mathematica software for the solutions of problems related to
ODEs. In particular, a chapter is devoted to the use ODEs and
Mathematica in the Dynamics of rigid bodies.
Mathematical methods and scientific computation are dealt with jointly
to supply a unified presentation. The main problems of ordinary
differential equations such
as, phase portrait, approximate solutions, periodic orbits, stability,
bifurcation, and
boundary problems are covered in an integrated fashion with numerous
worked examples and computer program demonstrations using
Mathematica.
Topics and Features:*Explains how to use the Mathematica package ODE.m
to support qualitative and quantitative problem solving *End-of-
chapter exercise sets incorporating the use of Mathematica programs
*Detailed description and explanation of the mathematical procedures
underlying the programs written in Mathematica *Appendix describing
the use of ten notebooks to guide the reader through all the
exercises.
This book is an essential text/reference for students, graduates and
practitioners in applied mathematics and engineering interested in
ODE's problems in both the qualitative and quantitative description of
solutions with the Mathematica program. It is also suitable as a self-
目次
Preface 1. Solutions of ODE's and Their Properties 2. Linear ODEs with Constant Coefficients 3. Power Series Solutions of ODEs and Frobenius Series 4. Poincare's Perturbation Method 5. Problems of Stability 6. Stability: The Critical Case 7. Bifurcation in ODEs 8. The Lindstedt-Poincare Method 9. Boundary-Value Problems for Second-Order ODEs 10. Rigid Body with a Fixed Point A. How to Use the Package ODE.m References Index
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