© 2014

A Short Course in Ordinary Differential Equations


  • Focuses on the theoretical aspect of ODEs without emphasis on lengthy technical applications of special equations from physics and engineering

  • Uses carefully selected and organized material to cover all significant text with analytic, easily comprehensible explanations

  • Simplifies and/or modifies many statements and proofs of theorems and introduces symbolic abbreviations for frequently used concepts and terms

  • Gives hints for proof-oriented exercises and answers to computational exercises


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


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.


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

Authors and affiliations

  1. 1.Department of Mathematical SciencesNorthern Illinois UniversityDeKalbUSA

About the authors

Qingkai Kong is a Professor and Director of Undergraduate Studies in the Department of Mathematical Sciences at Northern Illinois University. He holds a M.Sc and Ph.D from the University of Alberta. Dr. Kong is a recipient of the Huo Ying-Dong Teaching Award and has refereed for over 50 journals.

Bibliographic information


“All material is carefully organized and presented in a transparent manner. The text contains a large number of solved problems which illustrate well theoretical material. Each chapter concludes with a selection of exercises for independent study; hints and answers to exercises are collected in the end of the book along with a useful list of references and a subject index. … Undoubtedly, this book is a very valuable contribution to existing texts on qualitative theory of differential equations.” (Yuriy V. Rogovchenko, zbMATH, Vol. 1326.34007, 2016)