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Ordinary Differential Equations with Applications

  • Textbook
  • © 1999

Overview

Authors:
  1. Carmen Chicone

    1. Department of Mathematics, University of Missouri, Columbia, USA

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  • Many new exercises added

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

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xv
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  2. Introduction to Ordinary Differential Equations

    Pages 1-126

  3. Linear Systems and Stability

    Pages 127-197

  4. Applications

    Pages 199-282

  5. Hyperbolic Theory

    Pages 283-315

  6. Continuation of Periodic Solutions

    Pages 317-390

  7. Homoclinic Orbits, Melnikov’s Method, and Chaos

    Pages 391-450

  8. Averaging

    Pages 451-481

  9. Local Bifurcation

    Pages 483-529

  10. Back Matter

    Pages 531-561
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Keywords

About this book

This book is based on a two-semester course in ordinary di?erential eq- tions that I have taught to graduate students for two decades at the U- versity of Missouri. The scope of the narrative evolved over time from an embryonic collection of supplementary notes, through many classroom tested revisions, to a treatment of the subject that is suitable for a year (or more) of graduate study. If it is true that students of di?erential equations giveaway their point of viewbythewaytheydenotethederivativewith respecttotheindependent variable, then the initiated reader can turn to Chapter 1, note that I write x ?,not x , and thus correctly deduce that this book is written with an eye toward dynamical systems. Indeed, this book contains a thorough int- duction to the basic properties of di?erential equations that are needed to approach the modern theory of (nonlinear) dynamical systems. However, this is not the whole story. The book is also a product of my desire to demonstrate to my students that di?erential equations is the least insular of mathematical subjects, that it is strongly connected to almost all areas of mathematics, and it is an essential element of applied mathematics.

Authors and Affiliations

  • Department of Mathematics, University of Missouri, Columbia, USA

    Carmen Chicone

Bibliographic Information

  • Book Title: Ordinary Differential Equations with Applications

  • Authors: Carmen Chicone

  • Series Title: Texts in Applied Mathematics

  • DOI: https://doi.org/10.1007/b97645

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1999

  • eBook ISBN: 978-0-387-22623-1Published: 08 April 2008

  • Series ISSN: 0939-2475

  • Series E-ISSN: 2196-9949

  • Edition Number: 1

  • Number of Pages: XV, 563

  • Number of Illustrations: 5 b/w illustrations

  • Topics: Analysis

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