Just as before we substitute ux t f xg t into 428

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: λ = −n2 , f (x) = bn sin nx, where the bn ’s are constants. 101 for n = 1, 2, 3, . . . , 4.5.3. Find the function u(x, t), defined for 0 ≤ x ≤ π and t ≥ 0, which satisfies the following conditions: ∂2u ∂2u = , ∂t2 ∂x2 u(0, t) = u(π, t) = 0, u(x, 0) = sin x + 3 sin 2x − 5 sin 3x, ∂u (x, 0) = 0. ∂t 4.5.4. Find the function u(x, t), defined for 0 ≤ x ≤ π and t ≥ 0, which satisfies the following conditions: ∂2u ∂2u = , ∂t2 ∂x2 u(0, t) = u(π, t) = 0, ∂u (x, 0) = 0. ∂t u(x, 0) = x(π − x), 4.5.5. Find the function u(x, t), defined for 0 ≤ x ≤ π and t ≥ 0, which satisfies the following conditions: ∂2u ∂2u = , 2 ∂t ∂x2 u(0, t) = u(π, t) = 0, u(x, 0) = 0, ∂u (x, 0) = sin x + sin 2x. ∂t 4.5.6. (For students with access to Mathematica) a. Find the first ten coefficients of the Fourier sine series for h(x) = x − x4 by running the following Mathematica program f[n ] := 2 NIntegrate[(x - x∧4) Sin[n Pi x], {x,0,1}]; b = Table[f[n], {n,1,10}] b. Find the first ten terms of the solution to the initial value problem for a vi...
View Full Document

This document was uploaded on 01/12/2014.

Ask a homework question - tutors are online