Ordinary differential equations. (English) Zbl 0552.34001

Miller, Richard K.; Michel, Anthony N.

New York - London etc.: Academic Press (Harcourt Brace Jovanovich, Publishers). XIII, 351 p. (1982).

Some important examples of differential equations are given in the first chapter. Next two chapters contain the fundamental theory of linear and nonlinear differential equations. Linear boundary value problems are studied in Chapter 4. Lyapunov stability theory is discussed in Chapter 5. Chapter 6 contains perturbations of linear systems. Chapter 7 deals with the Poincaré-Bendixson theory and two-dimensional van der Pol type equations. The last chapter is devoted to the study of periodic solutions of general order systems. This book is intended as a text for a first graduate course in mathematics and applied sciences. The get-up is attractive.

Reviewer: K.Chandrasekhara Rao

MSC:

34-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations
34A30	Linear ordinary differential equations and systems, general
34A34	Nonlinear ordinary differential equations and systems, general theory
34A12	Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A05	Explicit solutions, first integrals of ordinary differential equations
34D20	Stability of solutions to ordinary differential equations
34C25	Periodic solutions to ordinary differential equations

Keywords:

examples; Lyapunov stability theory; Poincaré-Bendixson theory; two- dimensional van der Pol type equations