Ref.

This is the newest edition of George F. Simmons’s famous “Differential Equations with Applications and Historical Notes.” t drastically changed my outlook on a large part of mathematics. For example, we might wonder why do we put so much effort in studying the convergence of power series in analysis II? The subject is interesting on its own, but aside from the abstract interest, it’s ultimately because we want to use those methods to understand power series solutions of differential equations.
This book is clearly written, and it not only makes the subject interesting but deeply fascinating. Great mathematicians like Gauss and Laplace were trying to solve problems of physics and engineering, in which differential equations are ubiquitous, and these problems are the primary motivation for a large part of analysis and topology. Unlike other books on ODE, Simmons’ exercises are fun. It was fun just to read them, and each one got me excited to try to find out the answer.

I am aware that the university library has the first edition copy (1972), but this latest 3rd edition was augmented with a chapter dedicated to Laplace transform, improvements on the explanations of Abel’s mechanical problem, tautochrone, Van der Pol equations (Nonlinear dynamics-discussed in classical mechanics courses), and etc.

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