Myint-U T. Ordinary Differential Equations

Elsevier North Holland Inc., 1978. — 307 p. — ISBN: 0-444-00233-2.The theory of ordinary differential equations is one of the areas of mathematics that has long been studied, applied, and developed parallel to the natural sciences. Classical and modern treatments at both elementary and advanced levels have been widely published, yet there are only a few that have presented an introduction covering the essential topics of the theory of ordinary differential equations. The purpose of this text, therefore, is to present a fundamental theory of ordinary differential equations accompanied by an introduction to several important methods and techniques for determining solutions of a diverse class of equations.
The basic concepts and definitions of ordinary differential equations as well as mathematical models in population dynamics and celestial mechanics are presented in the first chapter. First-order equations with an emphasis on Picard's existence theorem are treated in chapter 2. The third chapter is concerned with classical methods for determining solutions of second-order linear equations together with the qualitative behavior of solutions of some types of equations. In chapter 4, equations with analytic coefficients are treated with Legendre and Bessel equations presented as examples of practical importance. Chapter 5 contains an analysis of systems of equations using matrices. Chapters 6 and 7 deal with boundary-value and eigenvalue problems, respectively. Stability of autonomous systems and the method of Lyapunov are the central themes of chapter 8. Chapter 9 describes the Laplace transform and its applications. Numerical solutions and error analyses are the main topics in the final chapter.
Exercises accompany each chapter and are an integral part of the text. They range from solving simple routine types of equations to proving more
difficult problems. Some minor topics are added to the exercises for an extended view of related subjects. Selected Solutions to Exercises and a
Bibliography appear at the end of the book.
This text is an outgrowth of lectures given at Manhattan College for mathematics and physics majors who normally have advanced calculus and
linear algebra in their third year. However, the text is designed for students with a good background in calculus and a knowledge of matrices.