This preview shows page 1. Sign up to view the full content.
Unformatted text preview: condition u ( x, 0) = f ( x ). This is a homogeneous linear partial dierential equation , second order in x and rst order in t . Just as for ODEs like u 00 ( t ) + 4 u = 0, we will seek special solutions and take a linear combination in order to get the general solution. We will then attempt to match the initial condition. The added complication is that there will be innitely many special solutions and force us to nd a Fourier series. The same teachiques can be used to discuss the motion of a vibrating string . See, for example, http://www.math.upenn.edu/ kazdan/260S12/notes/math21/math21-2012-2up.pdf (Math 21 Lecture Notes , Chapter 8.3, p. 369384) [Last revised: February 13, 2012] 1...
View Full Document
This note was uploaded on 03/06/2012 for the course MATH 260 taught by Professor Staff during the Spring '12 term at UPenn.
- Spring '12