This revised introduction to the basic methods, theory and applications of elementary differential equations employs a two part organization. Part I includes all the basic material found in a one semester introductory course in ordinary differential equations. Part II introduces students to certain specialized and more advanced methods, as well as providing a systematic introduction to fundamental theory.
A fantastic exposition to the subject, the rigorous development of the theory of linear DE is presented in the second half in a brief and comprehensive way. This is book contains the essential topics that are presented in a standard DE course, with the supplementary material of Sturm-Liouville problems, Fourier series, a very brief expositon of non-linear differential equations and a short introduction to PDE's.