A carefully revised edition of the well-respected ODE text, whose unique treatment provides a smooth transition to critical understanding of proofs of basic theorems. First chapters present a rigorous treatment of background material; middle chapters deal in detail with systems of nonlinear differential equations; final chapters are devoted to the study of second-order linear differential equations. The power of the theory of ODE is illustrated throughout by deriving the properties of important special functions, such as Bessel functions, hypergeometric functions, and the more common orthogonal polynomials, from their defining differential equations and boundary conditions. Contains several hundred exercises. Prerequisite is a first course in ODE.
This is a good text for a course in ODE after the computational course is completed. This book covers many topics in ODE, but be careful and watch for errors; especially near the end of the text. Most of the errors come in the excercises. For instance: you are asked to show that "every finite sequence of eigenfunctions of a S-L system is bounded". Duh! This is trivial until one realizes that every infinite sequence is also bounded.
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