The Calculus of Variations

The calculus of variations is a branch of math that deals with optimizing functions. It is the basis for problems like finding the shape of soap films and it forms the basis for Lagrangian dynamics.
Music "Everything" by Vi Hart
/ vihartvihart

[@spazmoidectomorf6209]

I like calculus of variations but i dont know how to learn it. What books do you recommend?

[@-ef]

At 4:11 I'm a little confused, wouldn't the equation hold true for any function of y when δy->0, and not necessarily one that minimizes I[y]?

[@shadowsniper5303]

It may help to think of delta I as a differential df. The derivative is 0 only at its minima. At all other points, there exists some h such that f(x+h) < f(x) and so the differential does not go to 0.