Topics

1

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"

2

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.

3

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?

4

Home Assignment 6 / Problem3

« on: November 07, 2012, 09:31:58 PM »

Solution is attached!

5

Misc Math / Fourier Transform

« on: November 05, 2012, 01:00:32 PM »

I was wondering (1/2 pi) in Fourier transform formula is an optional? (I mean, can we just ignore it?)

6

Home Assignment 5 / Problem4

« on: October 31, 2012, 09:31:34 PM »

Part (a) solution is attached!

7

Misc Math / TT1Problem6

« on: October 15, 2012, 01:33:57 PM »

In past term test 1, problem 6:

Write the solution of the diffusion equation on a half line 0<x<+∞,

I was wondering if we need to calculate integral on just 0<x<+∞ interval and not whole interval.

8

Home Assignment X / Problem2

« on: October 15, 2012, 01:34:28 AM »

Solution is attached,