Ordinary Differential Equations

Analysis, Qualitative Theory and Control

  • Hartmut Logemann
  • Eugene P. Ryan

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Hartmut Logemann, Eugene P. Ryan
    Pages 1-20
  3. Hartmut Logemann, Eugene P. Ryan
    Pages 21-64
  4. Hartmut Logemann, Eugene P. Ryan
    Pages 65-100
  5. Hartmut Logemann, Eugene P. Ryan
    Pages 101-166
  6. Hartmut Logemann, Eugene P. Ryan
    Pages 167-214
  7. Hartmut Logemann, Eugene P. Ryan
    Pages 215-258
  8. Back Matter
    Pages 259-333

About this book

Introduction

The book comprises a rigorous and self-contained treatment of initial-value problems for ordinary differential equations. It additionally develops the basics of control theory, which is a unique feature in the current textbook literature.

The following topics are particularly emphasised:

• existence, uniqueness and continuation of solutions,
• continuous dependence on initial data,
• flows,
• qualitative behaviour of solutions,
• limit sets,
• stability theory,
• invariance principles,
• introductory control theory,
• feedback and stabilization.

The last two items cover classical control theoretic material such as linear control theory and absolute stability of nonlinear feedback systems. It also includes an introduction to the more recent concept of input-to-state stability.

Only a basic grounding in linear algebra and analysis is assumed. Ordinary Differential Equations will be suitable for final year undergraduate students of mathematics and appropriate for beginning postgraduates in mathematics and in mathematically oriented engineering and science.

Keywords

Control Theory Feedback Lyapunov Stability Ordinary Differential Equations Stability Theory

Authors and affiliations

  • Hartmut Logemann
    • 1
  • Eugene P. Ryan
    • 2
  1. 1.Department of Mathematical SciencesUniversity of BathBathUnited Kingdom
  2. 2.Department of Mathematical SciencesUniversity of BathBathUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-6398-5
  • Copyright Information Springer-Verlag London 2014
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-6397-8
  • Online ISBN 978-1-4471-6398-5
  • Series Print ISSN 1615-2085
  • Series Online ISSN 2197-4144
  • About this book
Industry Sectors
Aerospace