Homework 10 collaboration area

Are there instructions on how to remotely access MAPEL anywhere? It would be nice to have access to check my work.

Login to software remote at the following link:

You will probably need to install the Citrix software. Once you do and are logged in, select

Applications -> Standard Software -> Computational Packages -> Maple 14

and the software will load remotely. Brig --Brericks 10:50, 30 October 2010 (UTC)

Another great resource I've found is:

but you will need to use Mathematica syntax there instead of MAPLE.

Question #14, is f(x) even? I know that pi*exp(-X) is neither odd or even, but when I graph the 2 conditions, they are symmetrical about the origin. To solve the problem, do I split up the integrals like Question #20?

Answer: Yes, the function is even because

$f(-x)=\pi e^{-(-x)}=\pi e^{x}=f(x)$

for a positive value of x. You can simplify your calculations by noting that the integral from minus L to plus L of an even function is equal to two times the integral from zero to L.

Question #17-18: Is there some way to "show" this analytically (given the hints), or should we just compute the first half-dozen terms and say "close enough"?

Answer: You will need to note that the Fourier Series converges to the function. After that, you'll need to plug in x=0 and x=1 and notice that the Fourier Series pops out the sum you are after. Page 482 is helpful.

--Plug x=0 and x=1 into what? Where do we do this? Thanks!
--Answer: Use Prob #3.
--Oh haha. I didn't realize we were supposed to use it for both. Thank you!

Question #20, The integral for a_o, a_n, and b_n involve a function that is zero from 0 to 2. How do I compute the integral?

Answer: You will just integrate from 2 to 4 instead of from 0 to 4.

Are we allowed to use Maple or MatLab to graph? Or should we hand-sketch the plots?

Answer from Bell: Yes, use MAPLE or Matlab or Mathematica or SAGE or whatever you know how to use. But don't sketch it by hand. That would be almost impossible.--Steve Bell 18:32, 2 November 2010 (UTC)

Alumni Liaison

To all math majors: "Mathematics is a wonderfully rich subject." Dr. Paul Garrett