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Misc Math / Re: Mean-value theorem
« on: November 27, 2012, 08:37:08 AM »
Here we integrate over V. Is this V the same as omega? And do we know if the coefficient c in G(x,y) is positive or negative? Thanks!
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Term Test 1 / Re: TT1 = Problem 1
« on: October 16, 2012, 08:42:02 PM »
I have a different solution for bonus
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Term Test 1 / Re: TT1 = Problem 5
« on: October 16, 2012, 08:23:50 PM »
I agree with Ian's solution. The value of H(x-y) depends on both x and y. So you have to break the scenarios regarding to x when doing the integral.
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Home Assignment 3 / Re: Problem 2
« on: October 10, 2012, 11:07:51 PM »
Here is my solution to this problem
I used the same approach as Zarak did, but in part (d) I think we would have to consider Dirichlet and Neumann boundary conditions separately. For Dirichlet, u(t,0)=> V(t,0) and we can use method of continuation to solve the V(x,t) first and then get u(x,t).
But for Neumann boundary condition, ux(t,0)=0 => nV(t,0) + Vx(t,0)=0 which does not necessarily mean that V(t,0)=0 or Vx(t,0)=0. In this case the boundary conditions are not automatically satisfied and we might not be able to use method of continuation.
Please let me know if there's anything wrong with this solution. Thanks in advance!
I used the same approach as Zarak did, but in part (d) I think we would have to consider Dirichlet and Neumann boundary conditions separately. For Dirichlet, u(t,0)=> V(t,0) and we can use method of continuation to solve the V(x,t) first and then get u(x,t).
But for Neumann boundary condition, ux(t,0)=0 => nV(t,0) + Vx(t,0)=0 which does not necessarily mean that V(t,0)=0 or Vx(t,0)=0. In this case the boundary conditions are not automatically satisfied and we might not be able to use method of continuation.
Please let me know if there's anything wrong with this solution. Thanks in advance!
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Home Assignment 2 / Re: Problem4
« on: October 01, 2012, 09:20:49 PM »
My solution on Problem 4. (2 parts) part1
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Home Assignment 2 / Re: Problem 3
« on: October 01, 2012, 09:11:43 PM »
Please see my solution on the attachment. 5 parts in total.
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Home Assignment 2 / Re: Problem 2
« on: September 30, 2012, 01:44:14 AM »
Could you give some hints to part (d)? I have r in the denominator and I was thinking if I can make the numerator equal 0 when r=0, so using L'hopital rule the limit might exist. Am I on the right track? Thank you.
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Home Assignment 1 / Re: Problem 4
« on: September 23, 2012, 04:21:38 AM »
But the only condition I have is the original PDE and my general solution just well satisfies that equation. What other conditions should I have? Thanks!
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