MA 3065 Final: hw4

• School: Minneapolis College of Art and Design
• Department: Filmmaking-Sound
• Course: MA 3065
• Professor: p

Document Summary

Math 5588 homework 4 (due thursday february 9: consider the following version of the isoperimetric problem: max u( 1)=0=u(1)z 1 u:[ 1,1] r. 1p1 + u (x)2 dx = l, where l > 2. Show that the optimal curve c(x) = (x, u(x)) must be a segment of a circle. [hint: proceed in a similar fashion to the brachistochrone problem. | u|2 dx subject to zu u2 dx = 1. Show that any minimizer is a solution of the eigenvalue problem ( u = u, u = 0, in u on u where > 0 is given by.