Burkill J.C. Theory of Ordinary Differential Equations

Oliver & Boyd, 1962. — 124 p.The aim of this text is to guide students in their quest for a more satisfying understanding of differential equations and their solutions. In the first chapter the existence of solutions of the simples! form of equation is established. Chapter II contains a systematic treatment of the linear equation. Chapter III (Oscillation Theorems) shows the reader that many properties of solutions of differential equations can be deduced directly from the equations. Chapters IV to VI deal with solutions in the form of series or integrals. A discussion of Legendre and Bessel functions (Chapters VII and VIII) illustrates the methods which have been developed and Chapter IX introduces the reader to asymptotic series. There is an appendix on the Laplace transform.