hw1 - Math 425/525, Spring 2011 Jerry L. Kazdan Problem Set...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 425/525, Spring 2011 Jerry L. Kazdan Problem Set 1 DUE: In class Thursday, Jan. 27. Late papers will be accepted until 1:00 PM Friday . 1. Find Green’s function g ( x , s ) to get a formula u ( x ) = R x 0 g ( x , s ) f ( s ) ds for a particular solution of u ±± ( x ) = f ( x ) . 2. In class we considered the oscillations of a weight attached to a spring hanging from the ceiling. If u ( t ) is the displacement of the mass m we were let to solve mu ( t ) = - ku , where k > 0 is a constant that depends on the stiffness of the spring. But this model neglected gravity. If we include gravity the equation becomes mu ±± = - ku + mg , where g is the gravitational constant, Solve this equation assuming you know the initial conditions u ( 0 ) = A and u ± ( 0 ) = B . 3. Let a ( x ) and f ( x ) be periodic functions with period P , so, for instance, a ( x + P ) = a ( x ) . This problem investigates periodic solutions u ( x ) (with period P ) of Lu : = u ± ( x )+ a ( x ) u = f ( x ) . a) Show there is a periodic solution of
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 03/06/2012.

Page1 / 2

hw1 - Math 425/525, Spring 2011 Jerry L. Kazdan Problem Set...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online