1

**Home Assignment 3 / Re: problem 3**

« **on:**December 18, 2012, 12:45:51 PM »

Solution to question3 part b is attached!

This section allows you to view all posts made by this member. Note that you can only see posts made in areas you currently have access to.

1

Solution to question3 part b is attached!

2

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**(-Ï•(xâˆ’ct)+Ï•(x+ct))**+ 1/2câˆ«ct+x0Ïˆ(s)ds +1/2câˆ«ctâˆ’x0Ïˆ(s)ds

instead of what you wrote:

"In our case correct formula is different

u(x,t)=1/2**(Ï•(xâˆ’ct)âˆ’Ï•(x+ct))**+ 1/2câˆ«ct+x0Ïˆ(s)ds +1/2câˆ«ctâˆ’x0Ïˆ(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

instead of what you wrote:

"In our case correct formula is different

u(x,t)=1/2

3

Dear professor Ivrii,

How do you suggest us to prepare for the final exam?

Does it have the same format as last year final exam?

Thank you so much for your time,

How do you suggest us to prepare for the final exam?

Does it have the same format as last year final exam?

Thank you so much for your time,

4

I was wondering if Cn has to be sin(nÎ¸) instead of cos(nÎ¸)?

5

Sorry to bother you,

Thank you,

Thank you,

Dear professor,

There is an announcement on the portal that we can go and get our TT2 papers today but I am just wondering if you are going to post our marks on the portal as well because some of us might not be able to go and pick up the test today?

Thank you kindly,

How should I know? I am in Stockholm. -- But actually marks were there, simply TAs forgot to remove the stealth cover from them.

6

Dear professor,

There is an announcement on the portal that we can go and get our TT2 papers today but I am just wondering if you are going to post our marks on the portal as well because some of us might not be able to go and pick up the test today?

Thank you kindly,

There is an announcement on the portal that we can go and get our TT2 papers today but I am just wondering if you are going to post our marks on the portal as well because some of us might not be able to go and pick up the test today?

Thank you kindly,

8

So, An is not zero when n=4k.

9

Please check the attachment!

11

Solution to (d) and (e) is attached!

12

In heat equation: We know IFT of e^ (-(Î¾^2)/2) is (âˆš2pi)e (-(x^2)/2). Then when we try to find IFT of e^ (-(ktÎ¾^2)), we scale Î¾ to âˆš(2kt)Î¾ and therefore x scale to âˆš(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.

13

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(nÏ€x/l)|^2"; Right?

Yes, except $\int_0^l |sin(nÏ€x/l)|^2\,dx =l/2$, 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.

14

I am just wondering in this question when P.T. wrote Parseval's equality, it shouldn't contain "integral |sin(nÏ€x/l)|^2"; Right?