An Introduction to Ordinary Differential Equations

  • Ravi P. Agarwal
  • Donal O'Regan

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages 1-12
  2. Pages 1-6
  3. Pages 7-12
  4. Pages 13-20
  5. Pages 61-67
  6. Pages 68-76
  7. Pages 144-151
  8. Pages 225-232
  9. Pages 240-249
  10. Pages 258-264
  11. Pages 279-285
  12. Back Matter
    Pages 1-12

About this book


This textbook provides a rigorous and lucid introduction to the theory of ordinary differential equations (ODEs), which serve as mathematical models for many exciting real-world problems in science, engineering, and other disciplines.

Key Features of this textbook:


Effectively organizes the subject into easily manageable sections in the form of 42 class-tested lectures

Provides a theoretical treatment by organizing the material around theorems and proofs

Uses detailed examples to drive the presentation

Includes numerous exercise sets that encourage pursuing extensions of the material, each with an "answers or hints" section

Covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics

Provides excellent grounding and inspiration for future research contributions to the field of ODEs and related areas


This book is ideal for a senior undergraduate or a graduate-level course on ordinary differential equations. Prerequisites include a course in calculus.


Series: Universitext

Ravi P. Agarwal received his Ph.D. in mathematics from the Indian Institute of Technology, Madras, India. He is a professor of mathematics at the Florida Institute of Technology. His research interests include numerical analysis, inequalities, fixed point theorems, and differential and difference equations. He is the author/co-author of over 800 journal articles and more than 20 books, and actively contributes to over 40 journals and book series in various capacities.

Donal O’Regan received his Ph.D. in mathematics from Oregon State University, Oregon, U.S.A. He is a professor of mathematics at the National University of Ireland, Galway. He is the author/co-author of 14 books and has published over 650 papers on fixed point theory, operator, integral, differential and difference equations. He serves on the editorial board of many mathematical journals.

Previously, the authors have co-authored/co-edited the following books with Springer: Infinite Interval Problems for Differential, Difference and Integral Equations; Singular Differential and Integral Equations with Applications; Nonlinear Analysis and Applications: To V. Lakshmikanthan on his 80th Birthday. In addition, they have collaborated with others on the following titles: Positive Solutions of Differential, Difference and Integral Equations; Oscillation Theory for Difference and Functional Differential Equations; Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations.


Algebra Boundary value problem calculus differential equation ordinary differential equation stability

Authors and affiliations

  • Ravi P. Agarwal
    • 1
  • Donal O'Regan
    • 2
  1. 1.Dept. Mathematical SciencesFlorida Institute of TechnologyMelbourneU.S.A.
  2. 2.University College GalwayNational University of IrelandGalwayIreland

Bibliographic information