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Scientific Computing with Mathematica®

Mathematical Problems for Ordinary Differential Equations

  • Book
  • © 2001

Overview

Authors:
  1. Addolorata Marasco

    1. Department of Mathematics, University of Naples, Naples, Italy

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    You can also search for this author in PubMed   Google Scholar

  2. Antonio Romano

    1. Department of Mathematics, University of Naples, Naples, Italy

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    You can also search for this author in PubMed   Google Scholar

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Solutions of ODEs and Their Properties

    • Addolorata Marasco, Antonio Romano
    Pages 1-31

  3. Linear ODEs with Constant Coefficients

    • Addolorata Marasco, Antonio Romano
    Pages 33-48

  4. Power Series Solutions of ODEs and Frobenius Series

    • Addolorata Marasco, Antonio Romano
    Pages 49-77

  5. Poincaré’s Perturbation Method

    • Addolorata Marasco, Antonio Romano
    Pages 79-98

  6. Problems of Stability

    • Addolorata Marasco, Antonio Romano
    Pages 99-125

  7. Stability: The Critical Case

    • Addolorata Marasco, Antonio Romano
    Pages 127-144

  8. Bifurcation in ODEs

    • Addolorata Marasco, Antonio Romano
    Pages 145-175

  9. The Lindstedt-Poincaré Method

    • Addolorata Marasco, Antonio Romano
    Pages 177-200

  10. Boundary-Value Problems for Second-Order ODEs

    • Addolorata Marasco, Antonio Romano
    Pages 201-230

  11. Rigid Body with a Fixed Point

    • Addolorata Marasco, Antonio Romano
    Pages 231-260

  12. Back Matter

    Pages 261-270
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Keywords

About this book

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-

Authors and Affiliations

  • Department of Mathematics, University of Naples, Naples, Italy

    Addolorata Marasco, Antonio Romano

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