Many interesting behaviors of real physical, biological,
economical, and chemical systems can be described by ordinary
differential equations (ODEs). Scientific Computing with
Mathematica 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 of 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 ODEs
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:
* Explanation of 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 of the mathematical procedures underlying
the twenty-eight 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 engineering and applied mathematics interested
in problems of ODEs in both the qualitative and quantitative
description of solutions with the Mathematica program. It is also
suitable as a self-study resource for professionals and others
seeking an understanding of how to use ODEs in modeling physical,
biological, and economic phenomena.
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