12-267/Homework Assignment 4: Difference between revisions

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This assignment is due at the tutorial on Tuesday October 16. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if your readers have a hard time deciphering your work they will give up and assume it is wrong.
This assignment is due at the tutorial on Tuesday October 16. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if your readers have a hard time deciphering your work they will give up and assume it is wrong.

Revision as of 13:37, 9 October 2012

This assignment is due at the tutorial on Tuesday October 16. Here and everywhere, neatness counts!! You may be brilliant and you may mean just the right things, but if your readers have a hard time deciphering your work they will give up and assume it is wrong.

Task 0. Identify yourself in the Class Photo!

Task 1. Find the general solution of the Euler-Lagrange equation corresponding to the functional , and investigate the special cases and .

Task 2. Find the extrema the following functional subject to and and .

Task 3. Solve the "power line problem": Of all the curves with and and with total arc-length , find the one with the least potential energy .


Task 4. Find a necessary condition for a function satisfying , , , and to be an extremal of a functional of the form .

Task 5. Find the curve joining the points and and for which the integral is minimal, if and .