Text:
Introduction to the Calculus of Variations
by Hans Sagan, Dover
Supplemental Text:
Convex Analysis and Variational Problems
by Ivar Ekeland and Roger Temam, SIAM
There are many problems that require one to find particular functions that minimize an integral. For example, among all paths connecting two points, which is the shortest? Given a path (which is described by a function of some sort) the distance along that path may be expressed as an integral of the function and its derivatives. The calculus of variations is about how to solve such problems. This will be an introductory course in the calculus of variations.
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Homework Assignment 1
Homework Assignment 2
The Hanging Chain
A Mathematica Notebook on the Hanging Chain