Unformatted text preview: condition u ( x, 0) = f ( x ). This is a homogeneous linear partial diﬀerential equation , second order in x and ﬁrst order in t . Just as for ODE’s 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 inﬁnitely many special solutions — and force us to ﬁnd 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/math2120122up.pdf (Math 21 Lecture Notes , Chapter 8.3, p. 369–384) [Last revised: February 13, 2012] 1...
View
Full Document
 Spring '12
 STAFF
 Math, Derivative, Fourier Series, Partial differential equation, Inner Products, Jerry L. Kazdan

Click to edit the document details