![]() Simmons’s “historical notes” often appear in footnotes. ![]() (The third edition adds some material from probability theory.) It’s hard going for a beginner, but it immediately establishes the main point: this stuff plays a central role in the physical sciences. Consider, for example, the first chapter, “The Nature of Differential Equations.” After the usual general remarks, Simmons provides examples: families of curves, growth and decay, chemical reactions, falling bodies, and (amazingly) the brachistochrone. Simmons’s book was very traditional, but was full of great ideas, stories, and illuminating examples. ![]() It was at that point that I ran into George Simmons’s Differential Equations with Applications and Historical Notes and fell in love with it. But very little stuck.Ī few years later I found myself needing to teach the basics of differential equations to a class of engineering students, part of their fourth semester calculus course. I did learn how to solve linear differential equations, and I remember the endless proof of existence and uniqueness of solutions, particularly the theorem that explained how the local solutions could be assembled into a solution that was valid in as large a region as possible. My first course in differential equations was a failure.
0 Comments
Leave a Reply. |