Practice problems for Exam 2 discussion area
Conversation between a student a Steve Bell:
> 1. for the sample midterm found here: > http://www.math.purdue.edu/~bell/MA527/prac2a.pdf > > For #3, what i tried to do is just do the > Laplace transform on each function and then > multiply them together.
Yes, that will give you the Laplace transform of the convolution. But they also want you to compute the (Laplace) convolution of those two functions. I did a problem exactly like that near the end of my lecture today. Note that, from the point of view of Laplace transforms u(t) times e^t is the same as e^t.
> For #6 I looked up Laplace for periodic > function and came across something totally > different.
The relevant formula is the last one on the cover page of the exam found at
http://www.math.purdue.edu/~bell/MA527/laplace.pdf
> For #10 I haven't completed it yet but my plan > was to plug in f(x) in Parseval's identity and > see if the summation of the coefficient and the > integral of the function will be the same.
That is the right idea. The left hand side will be bigger than something and the right hand side will be smaller than something, and you get an impossible situation.
> 2. for the mid term found here: > http://www.math.purdue.edu/~bell/MA527/mid2.pdf > > For #4-b we are asked to find the real Fourier > series from the complex one, is there a way to > do this without doing some of the calculation again.
I mentioned today that there will be no problems about the complex Fourier SERIES on Exam 2. The point of the question you refer to is that the integrals for the complex Fourier series are very easy to compute. To get the real Fourier series from it, you just expand the e^(inx) and e^(-inx) in terms of sine and cosine and then take the real part of what you get.
