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 Poincare-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.
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.
Preface.- Notation and Abbreviations.- 1. Initial Value Problems.- 2. Linear Differential Equations.- 3. Lyapunov Stability Theory.- 4. Dynamic Systems and Planar Autonomous Equations.- 5. Introduction to Bifurcation Theory.- 6. Second-Order Linear Equations.- Answers and Hints.- Bibliography.- Index.