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

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

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

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

View Full Document
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
Ask a homework question - tutors are online