Schwarzenberger R. Elementary Differential Equations 1969

Textbook in PDF format

This is an introductory book on differential equations which one can recommend enthusiastically. The author adopts a geometric approach to the subject and thereby achieves several commendable objectives. He points out by examples how mere manipulation of formulae can lead to meaningless solutions of differential equations, and shows how the student may avoid such pitfalls simply by drawing a few pictures. He also shows how to predict the shape of solution curves of differential equations by drawing a picture of the corresponding tangent field. In many cases this qualitative description is enough to answer the problem from which the differential equation arose, even though the student has no idea as to the “formula” for the solution. The student who acquires from this book even only these minimal qualitative ideas is likely to be better prepared to meet with differential equations in real life than his counterpart who has acquired a hotch-potch of special tricks for solving differential equations