Scientific Computing with Mathematica®: Mathematical Problems for Ordinary Differential Equations

✍ Scribed by Addolorata Marasco, Antonio Romano (auth.)

• Publisher: Birkhäuser Basel
• Year: 2001
• Tongue: English
• Leaves: 277
• Series: Modeling and Simulation in Science, Engineering and Technology
• Edition: 1
• Category: Library

✦ Synopsis

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-

✦ Table of Contents

Front Matter....Pages i-xiv
Solutions of ODEs and Their Properties....Pages 1-31
Linear ODEs with Constant Coefficients....Pages 33-48
Power Series Solutions of ODEs and Frobenius Series....Pages 49-77
Poincaré’s Perturbation Method....Pages 79-98
Problems of Stability....Pages 99-125
Stability: The Critical Case....Pages 127-144
Bifurcation in ODEs....Pages 145-175
The Lindstedt-Poincaré Method....Pages 177-200
Boundary-Value Problems for Second-Order ODEs....Pages 201-230
Rigid Body with a Fixed Point....Pages 231-260
Back Matter....Pages 261-270

✦ Subjects

Mathematical Modeling and Industrial Mathematics; Ordinary Differential Equations; Computational Science and Engineering; Applications of Mathematics; Appl.Mathematics/Computational Methods of Engineering; Math Applications in Computer S