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Do the same thing for <math>c_{-n}</math> and combine. | Do the same thing for <math>c_{-n}</math> and combine. | ||
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| + | Question: Page 506, Prob 15, if: | ||
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| + | <math>2a_o=\frac{2Pi^4}{9}</math> | ||
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| + | and | ||
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| + | <math>(a_n)^2=\frac{(4Pi^2)(cos)^2(nx)}{9}</math> | ||
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| + | I dont understand where the <math>\frac{Pi^4}{4}</math> comes from? Can anyone point out what I am doing wrong? | ||
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[[2010 MA 527 Bell|Back to the MA 527 start page]] | [[2010 MA 527 Bell|Back to the MA 527 start page]] | ||
Revision as of 07:26, 6 November 2010
Homework 11 collaboration area
Question: I'm having trouble getting HWK 11, Page 499, Problem 3 started.
Answer: You will need to use Euler's identity
$ e^{i\theta}=\cos\theta+i\sin\theta $
and separate the definitions of the complex coefficients into real and imaginary parts. For example,
$ c_n=\frac{1}{2L}\int_{-L}^L f(x)e^{-inx}\,dx= $
$ =\frac{1}{2L}\int_{-L}^L f(x)(\cos(-nx)+i\sin(-nx))\,dx= $
$ =\frac{1}{2L}\int_{-L}^L f(x)(\cos(nx)-i\sin(nx))\,dx= $
$ =\frac{1}{2L}(\int_{-L}^L f(x)(\cos(nx)\,dx - i\int_{-L}^L f(x)\sin(nx)\,dx)= $
$ =\frac{1}{2}(a_n-ib_n). $
Do the same thing for $ c_{-n} $ and combine.
Question: Page 506, Prob 15, if:
$ 2a_o=\frac{2Pi^4}{9} $
and
$ (a_n)^2=\frac{(4Pi^2)(cos)^2(nx)}{9} $
I dont understand where the $ \frac{Pi^4}{4} $ comes from? Can anyone point out what I am doing wrong?
