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Ordinary Differential Equations with Applications

  • Carmen Chicone

Part of the Texts in Applied Mathematics book series (TAM, volume 34)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Pages 225-322
  3. Pages 323-366
  4. Pages 511-543
  5. Pages 545-602
  6. Back Matter
    Pages 603-636

About this book

Introduction

This book developed over 20 years of the author teaching the course at his own university. It serves as a text for a graduate level course in the theory of ordinary differential equations, written from a dynamical systems point of view. It contains both theory and applications, with the applications interwoven with the theory throughout the text. The author also links ordinary differential equations with advanced mathematical topics such as differential geometry, Lie group theory, analysis in infinite-dimensional spaces and even abstract algebra.

The second edition incorporates corrections and improvements of the original text. New material includes a proof of the Grobman-Hartman theorem for flows based on the Lie derivative, more extensive treatment of the Euler-Lagrange equation and its applications, a proof of Noether's theorem on the existence of first integrals in the presence of symmetries and a new section on dynamic bifurcation with a proof of Pontryagin's formula.  The impressive array of existing exercises has been more than doubled in size and further enhanced in scope, providing mathematics, physical science and engineering graduate students with a thorough introduction to the theory and application of ordinary differential equations.

Reviews of the first edition:

``As an applied mathematics text on linear and nonlinear equations, the book by Chicone is written with stimulating enthusiasm. It will certainly appeal to many students and researchers.'' -- F. Verhulst, SIAM Review

``The author writes lucidly and in an engaging conversational style. His book is wide-ranging in its subject matter, thorough in its presentation, and written at a generally high level of generality, detail, and rigor.'' -- D. S. Shafer, Mathematical Reviews

Keywords

Derivative Implicit function Smooth function differential equation ordinary differential equation

Authors and affiliations

  • Carmen Chicone
    • 1
  1. 1.Department of MathematicsUniversity of MissouriColumbia

Bibliographic information

  • DOI https://doi.org/10.1007/0-387-35794-7
  • Copyright Information Springer Science+Business Media, Inc. 2006
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-30769-5
  • Online ISBN 978-0-387-35794-2
  • Series Print ISSN 0939-2475
  • Buy this book on publisher's site