### Author Topic: Problem 2  (Read 19855 times)

#### Fanxun Zeng

• Sr. Member
• Posts: 36
• Karma: 11
##### Re: Problem 2
« Reply #15 on: November 07, 2012, 10:26:05 PM »
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> Î²>0 2) Î² > w > 0 3) w<0 and |w|<|Î²| 4) w<0 and |w|>|Î²|  if we do want to divide. Thanks!
« Last Edit: November 07, 2012, 10:30:35 PM by Fanxun Peter Zeng »

#### Calvin Arnott

• Sr. Member
• Posts: 43
• Karma: 17
• OK
##### Re: Problem 2
« Reply #16 on: November 07, 2012, 11:54:42 PM »
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

• Sr. Member
• Posts: 51
• Karma: 9
##### Re: Problem 2
« Reply #17 on: November 08, 2012, 12:19:45 AM »
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

• Sr. Member
• Posts: 51
• Karma: 9
##### Re: Problem 2
« Reply #18 on: November 08, 2012, 12:21:22 AM »
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

• Full Member
• Posts: 17
• Karma: 3
##### Re: Problem 2
« Reply #19 on: November 14, 2012, 10:00:01 PM »
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

• Elder Member
• Posts: 2563
• Karma: 0
##### Re: Problem 2
« Reply #20 on: November 15, 2012, 01:21:59 AM »
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).
« Last Edit: November 15, 2012, 04:38:44 AM by Victor Ivrii »