hw6 - Math 260 Spring 2012 Jerry L Kazdan Problem Set 6 Due...

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

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.

Unformatted text preview: Math 260, Spring 2012 Jerry L. Kazdan Problem Set 6 Due: In class Thursday, Feb. 23. Late papers will be accepted until 1:00 PM Friday . Unless otherwise stated use the standard Euclidean norm . 1. Let u ( x,t ) be the temperature at time t at a point x on a homogeneous rod of length π , say 0 ≤ x ≤ π . Assume u satisfies the heat equation ∂u ∂t = ∂ 2 u ∂x 2 with boundary conditions u (0 ,t ) = 0 , ∂u ∂x vextendsingle vextendsingle vextendsingle vextendsingle x = π = 0 (so the right end is insulated) and initial condition u ( x, 0) = sin 5 2 x. a) Find the solution. b) Use Q ( t ) = 1 2 integraltext π u 2 ( x,t ) dx to prove there is at most one solution (uniqueness). 2. [Marsden-Tromba Sec. 2.4#1-2] Sketch the curves a ) . x = sin t, y = 4cos t, ≤ t ≤ 2 π b ) . x = 2sin t, y = 4cos t, ≤ t ≤ 2 π 3. Consider the curve F ( t ) = (sin2 t, 1 − 3 t, cos 2 t, 2 t 3 / 2 ) for 0 ≤ t ≤ 2 π . a) Find the equation of the tangent line at t = π/ 2....
View Full Document

{[ snackBarMessage ]}

Page1 / 3

hw6 - Math 260 Spring 2012 Jerry L Kazdan Problem Set 6 Due...

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

View Full Document
Ask a homework question - tutors are online