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3.6.2) GIVEN u(x₁ x ) = a₁ + a₂ n=1 .. 0₁ = ²5₁ 2 an a do = = [² f(x) dx = O n=D L = c = 1 angpy : 2. 늘 n=vo anfi ucx,t) = 2.L = O e-1,²+ = = 2.1 1 S cos (TTX) Cos (nπx) dx - (NTT) ² E Cos (¹) f(x)=COS (TTX) 200 COS TTX (DOESN'T = COS (NTTX) e (n=1) M AGREE WI a a -ant — Sin (TTX) | ! 55 COS (ITY) COS (MIX) dx L (IF n= m = 0) //=/22 (1Fh=m #0 ) (IFn&M) 2²2² = (NTT) = 0 2

3.6.2) GIVEN u(x₁ x ) = a₁ + a₂ n=1 .. 0₁ = ²5₁ 2 an a do = = [² f(x) dx = O n=D L = c = 1 angpy : 2. 늘 n=vo anfi ucx,t) = 2.L = O e-1,²+ = = 2.1 1 S cos (TTX) Cos (nπx) dx - (NTT) ² E Cos (¹) f(x)=COS (TTX) 200 COS TTX (DOESN'T = COS (NTTX) e (n=1) M AGREE WI a a -ant — Sin (TTX) | ! 55 COS (ITY) COS (MIX) dx L (IF n= m = 0) //=/22 (1Fh=m #0 ) (IFn&M) 2²2² = (NTT) = 0 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I'm trying to get confortbale with orthoginality properties of sin/cos functions. I'm working through this heat PDE problem and I found that the a_o coefficient is zero than in evaluating a_n I found that it doesn't agree. Shouldn't it? I can't see where I'm going wrong. THanks! (I highlighted to make it easier to find)

3.6.2) GIVEN u(x₁ x ) = a₁ + a₂ n=1 .. 0₁ = ²5₁ 2 an a do = = [² f(x) dx = O n=D L = c = 1 angpy : 2. 늘 n=vo anfi ucx,t) = 2.L = O e-1,²+ = = 2.1 1 S cos (TTX) Cos (nπx) dx - (NTT) ² E Cos (¹) f(x)=COS (TTX) 200 COS TTX (DOESN'T = COS (NTTX) e (n=1) M AGREE WI a a -ant — Sin (TTX) | ! 55 COS (ITY) COS (MIX) dx L (IF n= m = 0) //=/22 (1Fh=m #0 ) (IFn&M) 2²2² = (NTT) = 0 2
Transcribed Image Text:3.6.2) GIVEN u(x₁ x ) = a₁ + a₂ n=1 .. 0₁ = ²5₁ 2 an a do = = [² f(x) dx = O n=D L = c = 1 angpy : 2. 늘 n=vo anfi ucx,t) = 2.L = O e-1,²+ = = 2.1 1 S cos (TTX) Cos (nπx) dx - (NTT) ² E Cos (¹) f(x)=COS (TTX) 200 COS TTX (DOESN'T = COS (NTTX) e (n=1) M AGREE WI a a -ant — Sin (TTX) | ! 55 COS (ITY) COS (MIX) dx L (IF n= m = 0) //=/22 (1Fh=m #0 ) (IFn&M) 2²2² = (NTT) = 0 2
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By direct calculation a0=0 it is right.

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