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Who Solved the Bernoulli Differential Equation and How Did They Do It?

by Adam Parker

Year of Award: 2014

Award: Pólya

Publication Information: College Mathematics Journal, vol. 44, no. 2, March 2013, pp. 89-97.

Summary (adapted from the MAA Prizes and Awards booklet for MathFest 2014): Parker takes us on a mystery tour to seek to identify who was the first to actually solve Bernoulli’s Equation. You might think this entails nothing more than a careful search of very old publications seeking to find the first published solution, but there is much more to the story than that. Parker transports us to the 1690s, a world very different than the one we know today. Leibnitz and the Bernoulli brothers, Jacob and Johann, relate to one another as mentors, mentees, friends, and sometimes fierce competitors. Jacob poses the equation in print as a challenge problem. All three present solutions using a variety of techniques including reduction to a linear differential equation, separation of variables, and variation of parameters.

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About the Author: (From the MathFest 2014 MAA Prizes and Awards Booklet)

Adam Parker received B.S. degrees in Mathematics and Psychology from the University of Michigan in 1999, followed by his Ph.D. in Algebraic Geometry from the University of Texas at Austin in 2005. For the past 9 years he has been at Wittenberg University in Springfield, Ohio. A sepia dot (2006-07 Project NExT Fellow) he has been involved in several parts of the MAA, particularly the Ohio Section. He teaches a wide range of courses and often incorporates primary sources in his teaching. In his spare time, he enjoys sports, cooking, repairing old watches and spending time with his wife, Bernadette.

Subject classification(s): Differential & Difference Equations | Ordinary Differential Equations | Second Order ODEs | History of Mathematics
Publication Date: 
Friday, August 15, 2014