How Is Calculus of Variations Applied in Everyday Life?

[lover_of_math]

Calculus of Variation (pls help!)

hello! can somebody explain to me what's calculus of variation?? and more importantly, how it is applied in everyday life (such as consumer's products, industries etc) ? :) thanks so much! :!) really really need help!

 

[HallsofIvy]

You do understand that whole topics are written on this? I assume you know how to find maxima and minima for numerical functions. The basic problem in the calculus of variations is to find a function, y, that either maximizes or minimizes some "functional"- usually of the form
$$\int_a^bf(x,y,y')dx$$.

One example is finding the shape that a rope will make when hung between two poles. Another is finding the path down which an object will slide between two points in the least time (no, it's not a straight line. If the path is steep to start with the object will gain more speed to take it faster over the last part).

Here's a link to a simple explanation:
http://www.math.utah.edu/~hills/ez_cov/ez_cov.html

Google on "calculus of variations" for more information.