A first course in ordinary differential equations

Аннотация

The lecture notes presented here are intended for engineering and science students as a first course on differential equations. It is assumed that the students have already read a course on linear algebra, that included a discussion of general vector spaces, as well as a course on integral calculus for functions that depend on one variable. However, no previous knowledge of differential equations is required to read and understand this material. Many examples have been included in these notes and the proof of most statements are done in full details. The aim of the notes is to provide the student with a thorough understanding of the methods to obtain solutions of certain classes of differential equations, rather than the qualitative understanding of solutions and their existence. With the exception of some nonlinear first-order differential equations, we concentrate on linear differential equations and the derivation of their solutions.