Scientific Computing with Mathematica®

Antonio Romano

ISBN 10: 1461266351 / ISBN 13: 9781461266358

Editore: Birkhäuser Boston, Birkhäuser Boston Apr 2013, 2013

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Neuware -Many interesting behaviors of real physical, biological, economicaland chemical systems can be described by ordinary differentialequations (ODEs).Scientific Computing with Mathematica for Ordinary DifferentialEquationsprovides a general framework useful for the applications, on theconceptual aspects of the theory of ODEs, as well as a sophisticateduse of Mathematica software for the solutions of problems related toODEs. In particular, a chapter is devoted to the use ODEs andMathematica in the Dynamics of rigid bodies.Mathematical methods and scientific computation are dealt with jointlyto supply a unified presentation. The main problems of ordinarydifferential equations suchas, phase portrait, approximate solutions, periodic orbits, stabilitybifurcation, andboundary problems are covered in an integrated fashion with numerousworked examples and computer program demonstrations usingMathematica.Topics and Features:\*Explains how to use the Mathematica package ODE.mto support qualitative and quantitative problem solving \*End-ofchapter exercise sets incorporating the use of Mathematica programs\*Detailed description and explanation of the mathematical proceduresunderlying the programs written in Mathematica \*Appendix describingthe use of ten not Elektronisches Buch to guide the reader through all theexercises.This book is an essential text/reference for students, graduates andpractitioners in applied mathematics and engineering interested inODE's problems in both the qualitative and quantitative description ofsolutions with the Mathematica program. It is also suitable as a self-Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 288 pp. Englisch.

Codice articolo 9781461266358

Dati bibliografici

• Titolo: Scientific Computing with Mathematica®
• Editore: Birkhäuser Boston, Birkhäuser Boston Apr 2013
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 1461266351
• ISBN 13: 9781461266358
• Rilegatura: Taschenbuch
• Condizione: Neu

Descrizione articolo

Riassunto

Provides a general framework useful for the application of the theory of ODEs, as well as a sophisticated use of Mathematica software for the solution of problems related to ODEs. Through extensive worked examples and computer program demonstrations using Mathematica, the authors cover phase portrait, approximate solutions, periodic orbits, stability, bifurcation, and boundary problems. For graduate students, researchers, and practitioners in applied mathematics and engineering seeking an understanding of using ODEs in modeling physical, biological, and economic phenomena.

Contenuti

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. Poincaré's Perturbation Method 5. Problems of Stability 6. Stability: The Critical Case 7. Bifurcation in ODEs 8. The Lindstedt-Poincaré 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