Solve the heat equation k a²u 0x² u(x, t) = = u(0, t) = 0, u(L, t) = 0, 0 0 (see (1) in Section 12.3) subject to the given conditions. Assume a rod of length L. at t > 0 Σ( n = 1 1)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 44E
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Solve the heat equation k
a²u
0x²
u(x, t) =
=
u(0, t) = 0, u(L, t) = 0, t > 0
u(x, 0) = {1, 1/2XX<²
0<x<L/2
+
au
du, 0<x<L, t> 0 (see (1) in Section 12.3) subject to the given conditions. Assume a rod of length L.
at
Σ(
n = 1
1)
Transcribed Image Text:Solve the heat equation k a²u 0x² u(x, t) = = u(0, t) = 0, u(L, t) = 0, t > 0 u(x, 0) = {1, 1/2XX<² 0<x<L/2 + au du, 0<x<L, t> 0 (see (1) in Section 12.3) subject to the given conditions. Assume a rod of length L. at Σ( n = 1 1)
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