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517: 5. See page 2 of Bell's 11/10/2010 lecture at | 517: 5. See page 2 of Bell's 11/10/2010 lecture at | ||
| − | |||
[http://www.math.purdue.edu/~bell/MA527/Lectures/lec11-10.pdf Lesson 33] | [http://www.math.purdue.edu/~bell/MA527/Lectures/lec11-10.pdf Lesson 33] | ||
517: 7. See | 517: 7. See | ||
| + | [http://www.math.purdue.edu/~bell/MA527/HWK/p517_7.pdf p. 517: 7 Solution] | ||
| − | [http://www.math.purdue.edu/~bell/MA527/ | + | And for solutions to the three problems on p. 528, go to |
| + | [http://www.math.purdue.edu/~bell/MA527/jing Bell's Jing things] | ||
[[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 10:28, 12 November 2010
Homework 12 Solutions
517: 1.
$ \hat{f}_c(w)=\sqrt{\frac{2}{\pi}}\left( \int_0^1(-1)\cos(wx)\,dx+ \int_1^2(1)\cos(wx)\,dx \right)= $
$ =\sqrt{\frac{2}{\pi}}\left([-\frac{1}{w}\sin(wx)]_0^1 +[\frac{1}{w}\sin(wx)]_1^2\right)= $
$ =\sqrt{\frac{2}{\pi}}\ \frac{1}{w}\left( -(\sin(w)-0)+(\sin(2w)-\sin(w)) \right)= $
$ =\sqrt{\frac{2}{\pi}}\ \frac{\sin(2w)-2\sin(w)}{w}. $
517: 2.
$ \hat{f}_c(w)=\sqrt{\frac{2}{\pi}}\left( \int_0^k x\cos(wx)\,dx\right)= $
$ =\sqrt{\frac{2}{\pi}}\left(\left[\frac{x}{w}\sin(wx)+\frac{1}{w^2}\cos(wx)\right]_0^k \right)= $
$ \sqrt{\frac{2}{\pi}}\left(\frac{k}{w}\sin(kw)+\frac{1}{w^2}\cos(kw) -\frac{1}{w^2}\right). $
517: 5. See page 2 of Bell's 11/10/2010 lecture at Lesson 33
517: 7. See p. 517: 7 Solution
And for solutions to the three problems on p. 528, go to Bell's Jing things
