Category: Mathematical Physics Description: In calculus, you learned how to minimize or maximize an individual function. Have you ever wondered how to minimize or maximize the integral of a function? There is a remarkable simple method, due to Euler and Lagrange, which remarkably lets us derive planetary motion, newtonian mechanics, and the movements of soap bubbles, all from very simple assumptions. Structure: I will first give an overview of what we can learn by minimizing integrals. Students will then complete "fill-in-the-blank" proofs and example exercises. Then, each student will be given a different problem to work on, to share with their table once they're done.