Albion College

Mathematics and Computer Science

Mathematics and Computer Science

COLLOQUIUM

Finding the Best Way From Here to There — A Primer on Variational Calculus

Darren Mason

Given a task to accomplish, it is natural to ask what is the **best** way to achieve your goal? Maybe you are flying from Beijing to London and need the shortest flight path. Or you are selling fuel and you want to find the optimal time *t* to sell it so that you can maximize your profit. Or you are crossing a river with a strong current and want to determine a propeller direction (as a function of time) so that you cross the river in the least amount of time. The number of possible questions of this type seems endless. During this lecture we will discuss some of the above problems, a famous brain-teaser called the *brachistochrone problem*, and illustrate how to find solutions to these problems using a version of calculus that makes sense in infinite dimensions — the interesting field of variational calculus!