978-0-486-63828-7 / 9780486638287

Ordinary Differential Equations and Stability Theory: An Introduction


Publisher:Dover Publications



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SUB-TITLE: An Introduction. ALSO KNOWN AS: This Dover edition, first published in 1979, s an unabridged and unaltered republication of the work originally published in 1968 by W. H. Freeman and Company. CONTENTS: Chapter 1 Introduction; Chapter 2 The Linear Equation: General Discussion; Chapter 3 The Linear Equation with Constant Coefficients; Chapter 4 Autonomous Systems and Phase Space; Chapter 5 Stability for Nonautonomous Equations; Chapter 6 Existence, Uniqueness, and Related Topics; Appendix A Series Solutions of Second-Order Linear Equations; Appendix B Linear Systems with Periodic Coefficients; References; Index. PUBLISHER: Dover Publications, Inc. New York. A DOVER EDITION DESIGNED FOR YEARS OF USE! We have made every effort to make this the best book possible. Our paper is opaque, with minimal show-through; it will not discolor or become brittle with age. Pages are sewn in signatures, in the method traditionally used for the best books, and will not drop out, as often happens with paperbacks held together with glue. Books open flat for easy reference. The binding will not crack or split. This is a permanent book. SYNOPSIS: This is a brief, modern introduction to the subject of ordinary differential equations, with an emphasis on stability theory. Concisely and lucidly expressed, it is intended as a supplementary text for the advanced undergraduate or beginning graduate student who has had a first course in ordinary differential equations. The author begins with a discussion of the linear system x = A(t)x and develops the notions of a fundamental system of solutions, the Wronskian, and the corresponding fundamental matrix. He then introduces the nonhomogeneous linear equation and the important variation of parameters formula, by which, following a consideration of the nth-order linear equation, the solution of the nonhomogeneous nth-order linear equation is obtained. A chapter is then devoted to the linear equation with constant...

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