The Simmons book is clearly written, and it not only makes the subjectinteresting 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. By page 30 Simmons hastreated falling objects with air resistance and shown how to calculateterminal velocities. After spending all of high school doing falling-objects problems without air resistance, it was a relief to finally do them right.Another early highlight is the solution of the famous brachistochrone problem, something I had been wondering for years.
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