This coherent, balanced presentation examines the theory, applications, and techniques of differential equations. Intended for use in introductory courses, the text focuses on initial- and boundary-value problems, general properties of linear equations, and the differences between linear and nonlinear systems. Well-defined techniques include careful explanations of conditions for applicability, with emphasis on methods of general use rather than specific methods of limited use.
Topics include basic concepts; special methods for first-order equations, and the applications of these equations; existence, uniqueness, and methods of approximation; linear differential equations; applications of second-order linear differential equations; the Laplace transform; boundary-value problems; partial differential equations of mathematical physics; and more.
Covering far more material than is customary for an introductory work, the text includes a remarkably large number of illustrative examples worked out in detail and extensive sets of problems. Answers or hints to most of the problems appear at the end.
Reprint of the McGraw-Hill Book Company, New York, 1968 edition.