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### Messages - Kun Guo

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##### Home Assignment 9 / Problem 2
« on: December 03, 2012, 09:38:29 PM »
http://www.math.toronto.edu/courses/apm346h1/20129/HA9.html#problem-9.2

For U3, there shouldn't be a log; and for U2, it should be (1/2*pi)* log[(x^2+y^2)^(1/2)], right?

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##### Misc Math / Re: Mean-value theorem
« on: November 25, 2012, 05:46:40 PM »
thanks professor, now it makes more sense

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##### Misc Math / Mean-value theorem
« on: November 24, 2012, 06:23:08 PM »
I do not quite understand step b and c(see attached) in the proof of Mean-value theorem. Did you use Green's identity or some other identity when dragging out terms from the integral?

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##### Misc Math / Re: 2011 term test 2 Problem 3. d
« on: November 15, 2012, 11:49:27 AM »
Yes I got X0(t)T0(t)=cos(1/2*x)*exp(-1/2*t). But one solutions posted last year have either 0 or pi/2...

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##### Misc Math / 2011 term test 2 Problem 3. d
« on: November 14, 2012, 10:41:56 PM »
utâˆ’kuxx=0 for xâˆˆ(0,Ï€)
with the boundary conditions ux(0,t)=0 and u(Ï€,t)=0 and the initial condition u(x,0)=x.

Part d) Write the solution in the form of a series.

If we use separation of variables, U=X*T, I found that T0 is t dependent. Then A0*T0 cannot not just a constant or zeor(A0 is for X).
Are there any mistakes regarding that part in both solutions poster last year?

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##### Home Assignment 6 / Re: Problem 2
« 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.

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##### Misc Math / Lec 23 Possion formula clarification
« on: November 10, 2012, 05:33:03 PM »
Attached picture is a screen shot of online notes lecture 23. I was wondering if there is an addition r in front of sin(n*theta) in (12). Also, is there missing a^(-n) in calculating An and Cn?

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##### Home Assignment 7 / Problem 1
« on: November 10, 2012, 03:51:49 PM »
why in problem 1 we are looking for 'solutions' instead of a single solution?

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##### Home Assignment 6 / Problem 4
« on: November 05, 2012, 11:41:38 PM »
For part c, sinx/x is an even function and its integral is Si(x). Then should we simply get positive infinity?

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##### Home Assignment 4 / Re: Problem 1
« on: October 19, 2012, 12:26:33 AM »
for part a, should we add a condition that alpha and beta are real? Or they have to be real since we are assuming all eigenvalues are real?

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##### Home Assignment 2 / Re: Problem 1
« on: October 15, 2012, 09:33:18 PM »
Build on DW's solution,part c).  For -2t < x < 2t, x+3t> 0, Ï• can be solved the same as in part a). x+2t<0, Ïˆ is the same as x< -2t, which is a constant C, since Ï•+Ïˆ.  The u(x,t)= 1/4exp(-x-2t)+C for -2t < x < 2t. Will this be a correct answer to finish up the question?

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##### Home Assignment X / Re: problem 3
« on: October 15, 2012, 08:42:24 PM »
will alpha: non-negative and beta:non-positive for part b) be a more accurate answer?

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##### Home Assignment 3 / Re: Problem 1
« on: October 05, 2012, 12:22:45 AM »
I think there is still problem 2/ sqrt(pi) instead of sqrt(2/pi), is this true?

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##### Home Assignment 3 / Problem 1
« on: October 04, 2012, 05:47:45 PM »
I noticed the given error function(Erf) in the problem set sheet is different with what's given in WolframAlpha. Which one should I use? Also, are we expected to write our final answers in form of Erf?

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##### Home Assignment 2 / Problem 2
« on: September 27, 2012, 12:45:31 AM »
It looks like I should use the result from part 3 for part 4. However if so, how should I use the initial values?

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