(New page: == Homework 11 collaboration area == Back to the MA 527 start page To Rhea Course List Category:MA5272010Bell) |
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== Homework 11 collaboration area == | == Homework 11 collaboration area == | ||
| + | Question: I'm having trouble getting HWK 11, Page 499, Problem 3 started. | ||
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| + | Answer: You will need to use Euler's identity | ||
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| + | <math>e^{i\theta}=\cos\theta+i\sin\theta</math> | ||
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| + | and separate the definitions of the complex coefficients into real and imaginary parts. For example, | ||
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| + | <math>c_n=\frac{1}{2L}\int_{-L}^L f(x)e^{-inx}\,dx=</math> | ||
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| + | <math>=\frac{1}{2L}\int_{-L}^L f(x)(\cos(-nx)+i\sin(-nx))\,dx=</math> | ||
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| + | <math>=\frac{1}{2L}\int_{-L}^L f(x)(\cos(nx)-i\sin(nx))\,dx=</math> | ||
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| + | <math>=\frac{1}{2}(a_n-ib_n).</math> | ||
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| + | Do the same thing for <math>c_{-n}</math> and combine. | ||
[[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 06:44, 5 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}{2}(a_n-ib_n). $
Do the same thing for $ c_{-n} $ and combine.
