|Calculus and Its Origins now includes material on the origins of differential equations! The author, Dave Perkins, explains how he gathered the information with the help of his colleagues below.
"In the months after Calculus & Its Origins was initially printed, I gradually grew sorry that I had not included any material concerning the origins of differential equations. It's my understanding that calculus was born not only out of pure curiosity but also, more importantly, out of the desire to quantify scientific observations. Differential equations are the calculus-based expression of such observations.
When I learned that the book would be reprinted, I eagerly asked for permission to include a few pages on the subject. The MAA folks graciously agreed. On the very day I asked, I opened the March 2013 College Mathematics Journal to the article "Who solved the Bernoulli differential equation and how did they do it?" by Adam Parker. What amazing luck! Even better, Adam agreed to talk to me on the phone, whereupon he helped me to sort out my ideas for the new material I wished to include in the second printing.
I eventually chose several of the earliest differential equations to outline as exercises (all exercises in the book are extended outlines of some historically important result, rather than being simply lists of practice questions). The first exercise describes Descartes's solution to a problem posed to him by Florimund de Beaune, a man of many interests whose differential equation related to the behavior of sound. The other problems concern equations posed by two of the Bernoulli brothers.
Time was short, so I posted a plea for help to my Project NExT email group, wondering if perhaps a person or two could look at my first draft of these problems over the ensuing 36 hours. Not only did I get immediate offers, but two group members cross-posted my request to other lists. Soon I had a dozen confirmed helpers who committed to my quick time frame.
The offers kept coming, and I told each person that I had plenty of help, but would send them my material if they'd like to see it nevertheless. Every one said, "Please do send the problems. I'd like to see them!" To me, this testifies to both a widespread love for the history of mathematics and the collegiality that I have always encountered among mathematicians. This warmth and this curiosity are what prompted me to ask if I could write this blog post, to share my feel-good story and publicly say thank you.
My colleagues who reacted so quickly and in such caring detail to my new material are now listed in the preface of the second edition, but I want to thank them again. They are Adam Parker, Jennifer Daniel, William Dunham, Melissa Hoover, Lynne Ipina, Dan Kemp, Will Murray, and Fred Rickey.
My thanks as well to Carol Baxter and Beverly Ruedi at the MAA for their efforts in including the new material."