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A Short Course in Ordinary Differential Equations

  • Qingkai Kong

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Qingkai Kong
    Pages 1-29
  3. Qingkai Kong
    Pages 31-60
  4. Qingkai Kong
    Pages 61-100
  5. Qingkai Kong
    Pages 167-201
  6. Qingkai Kong
    Pages 203-250
  7. Back Matter
    Pages 251-267

About this book

Introduction

This text is a rigorous treatment of the basic qualitative theory of ordinary differential equations, at the beginning graduate level. Designed as a flexible one-semester course but offering enough material for two semesters, A Short Course covers core topics such as initial value problems, linear differential equations, Lyapunov stability, dynamical systems and the Poincaré—Bendixson theorem, and bifurcation theory, and second-order topics including oscillation theory, boundary value problems, and Sturm—Liouville problems. The presentation is clear and easy-to-understand, with figures and copious examples illustrating the meaning of and motivation behind definitions, hypotheses, and general theorems. A thoughtfully conceived selection of exercises together with answers and hints reinforce the reader's understanding of the material. Prerequisites are limited to advanced calculus and the elementary theory of differential equations and linear algebra, making the text suitable for senior undergraduates as well.

Keywords

Lyapunov function method Poincaré-Bendixson theorem Sturm–Liouville problems bifurcation theory linear differential equations stability theory

Authors and affiliations

  • Qingkai Kong
    • 1
  1. 1.Department of Mathematical SciencesNorthern Illinois UniversityDeKalbUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-11239-8
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-11238-1
  • Online ISBN 978-3-319-11239-8
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site