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Differential Equations: Theory and Applications

  • David Betounes

Table of contents

  1. Front Matter
    Pages 1-13
  2. David Betounes
    Pages 1-35
  3. David Betounes
    Pages 37-78
  4. David Betounes
    Pages 79-117
  5. David Betounes
    Pages 119-219
  6. David Betounes
    Pages 221-266
  7. David Betounes
    Pages 267-332
  8. David Betounes
    Pages 333-370
  9. David Betounes
    Pages 371-474
  10. David Betounes
    Pages 475-534
  11. David Betounes
    Pages 535-552
  12. David Betounes
    Pages 553-577
  13. David Betounes
    Pages 579-611
  14. David Betounes
    Pages 613-614
  15. Back Matter
    Pages 1-11

About this book

Introduction

The book provides a comprehensive introduction to the theory of ordinary differential equations at the graduate level and includes applications to Newtonian and Hamiltonian mechanics. It not only has a large number of examples and computer graphics, but also has a complete collection of proofs for the major theorems, ranging from the usual existence and uniqueness results to the Hartman-Grobman linearization theorem and the Jordan canonical form theorem.

The book can be used almost exclusively in the traditional way for graduate math courses, or it can be used in an applied way for interdisciplinary courses involving physics, engineering, and other science majors. For this reason an extensive computer component using Maple is provided on Springer’s website.

This new edition has been extensively revised throughout, particularly the chapters on linear systems, stability theory and Hamiltonian systems.

The computer component is an in-depth supplement and complement to the material in the text and contains an introduction to discrete dynamical systems and iterated maps, special-purpose Maple code for animating phase portraits, stair diagrams, N-body motions, and rigid-body motions, and numerous tutorial Maple worksheets pertaining to all aspects of using Maple to study the topics in the text.

Review from first edition:

"This book is intended for first- and second- year graduate students in mathematics and also organized to be used for interdisciplinary courses in applied mathematics, physics, and engineering. ... The book is well written and provides many interesting examples. The author gives a comprehensive introduction to the theory on ordinary differential equations with a focus on mechanics and dynamical systems. The exposition is clear and easily understood...." (Yuan Rong, Zentralblatt MATH, Vol. 993 (18), 2002)

Keywords

Betounes Differential Equations Dynamical Systems Stability theory Systems of Differential Equations The flow generated by a vector field Vector Fields ordinary differential equation

Authors and affiliations

  • David Betounes
    • 1
  1. 1.Dept. Physics, Astronomy &, GeosciencesValdosta State UniversityValdostaUSA

Bibliographic information