Problem 2

[Fanxun Zeng]

I agree with Ziting Zhou that we CAN divide 4 cases in part d if we wish, exactly what I did. Let me show mathematically what the four cases are: 1) w> β>0 2) β > w > 0 3) w<0 and |w|<|β| 4) w<0 and |w|>|β|  if we do want to divide. Thanks!

[Calvin Arnott]

Calvin, if you type your solutions in LaTeX or TeX, you could post just the source fixing some discrepancies on the fly

I changed the .pdfs to png's for now, when I have some time later I'll try to massage the tex code into mathjax/forum format.

[Zarak Mahmud]

Aida: How did you do the integral?

He didn't. He used a fourier transform pair from part 1(a).

Yes, That's right!
By the way Zarak, I guess it is clear from my name that I am female!

Hahah oops, sorry!

[Zarak Mahmud]

Calvin, if you type your solutions in LaTeX or TeX, you could post just the source fixing some discrepancies on the fly

I changed the .pdfs to png's for now, when I have some time later I'll try to massage the tex code into mathjax/forum format.

Calvin - just curious, what program are you in?

[Kun Guo]

Same question as Ziting, should there be four cases regarding  beta and +/- omega relationship? The sign will change when we get rid of the absolute sign and take the derivative.

[Victor Ivrii]

Same question as Ziting, should there be four cases regarding  beta and +/- omega relationship? The sign will change when we get rid of the absolute sign and take the derivative.

You don't need any divisions, just apply properties. And I already demonstrated http://www.math.toronto.edu/courses/apm346h1/20129/L17.html#sect-17.4
that if we consider integrals in the sense of usual improper integrals they will not converge as $\omega=\pm \beta$ while in the sense of the principal value they will (not required).