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Home Assignment 3 / Re: problem 3
« on: December 18, 2012, 12:45:51 PM »
Solution to question3 part b is attached!
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Misc Math / Last year FinalExam
« on: December 13, 2012, 01:56:49 PM »
http://weyl.math.toronto.edu:8888/APM346-2011F-forum/index.php?topic=208.0
In last year final exam, problem 1, when you solved it by method of continuation, I was wondering if the first term will be:
u(x,t)=1/2(-ϕ(x−ct)+ϕ(x+ct))+ 1/2c∫ct+x0ψ(s)ds +1/2c∫ct−x0ψ(s)ds
instead of what you wrote:
"In our case correct formula is different
u(x,t)=1/2(ϕ(x−ct)−ϕ(x+ct))+ 1/2c∫ct+x0ψ(s)ds +1/2c∫ct−x0ψ(s)ds"
In last year final exam, problem 1, when you solved it by method of continuation, I was wondering if the first term will be:
u(x,t)=1/2(-ϕ(x−ct)+ϕ(x+ct))+ 1/2c∫ct+x0ψ(s)ds +1/2c∫ct−x0ψ(s)ds
instead of what you wrote:
"In our case correct formula is different
u(x,t)=1/2(ϕ(x−ct)−ϕ(x+ct))+ 1/2c∫ct+x0ψ(s)ds +1/2c∫ct−x0ψ(s)ds"
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Misc Math / Re: Lec 23 Possion formula clarification
« on: December 08, 2012, 01:10:03 PM »
I was wondering if Cn has to be sin(nθ) instead of cos(nθ)?
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Term Test 2 / Re: TT2--Problem 2
« on: November 18, 2012, 07:39:15 PM »
So, An is not zero when n=4k.
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Term Test 2 / Re: TT2--Problem 2
« on: November 18, 2012, 07:37:19 PM »
Please check the attachment!
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Term Test 2 / Re: TT2--Problem 2
« on: November 18, 2012, 01:47:40 PM »
Solution to (d) and (e) is attached!
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Misc Math / Lecture 19
« on: November 13, 2012, 03:12:17 PM »
In heat equation: We know IFT of e^ (-(ξ^2)/2) is (√2pi)e (-(x^2)/2). Then when we try to find IFT of e^ (-(ktξ^2)), we scale ξ to √(2kt)ξ and therefore x scale to √(2kt)x. But in the lecture note, it is mentioned that x scale to (2kt)^(-1/2)x. I believe it should be just square root of 2kt and not (-square root) of 2kt.
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Misc Math / Re: Last Year HW:5.4.12
« on: November 12, 2012, 11:57:41 AM »Aida, please next time provide a link, like this one
http://weyl.math.toronto.edu:8888/APM346-2011F-wiki/index.php/Home_Assignment_8#5.4.12.I am just wondering in this question when P.T. wrote Parseval's equality, it shouldn't contain "integral |sin(nπx/l)|^2"; Right?
Yes, except $\int_0^l |sin(nπx/l)|^2\,dx =l/2$, so you don't need this integral. Ditto for 5.4.13, 5.4.15.
And who is P.T.?
"Paul Tan" Last year student.
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Misc Math / Last Year HW:5.4.12
« on: November 11, 2012, 10:33:08 PM »
I am just wondering in this question when P.T. wrote Parseval's equality, it shouldn't contain "integral |sin(nπx/l)|^2"; Right?
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Home Assignment 6 / Re: Problem 2
« on: November 07, 2012, 09:49:47 PM »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!