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Answer: The problem says that it is fixed at U1 and U2 for all time. I interpret this as X(0)=U1 and X(L)=U2, and X'(0)=X'(L)=0 since they are not changing at those points. Apply these to the X equation after you separate your variables. The T equation will come out the same as before. | Answer: The problem says that it is fixed at U1 and U2 for all time. I interpret this as X(0)=U1 and X(L)=U2, and X'(0)=X'(L)=0 since they are not changing at those points. Apply these to the X equation after you separate your variables. The T equation will come out the same as before. | ||
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| + | RESPONSE: I don't think that X'(0)=X'(L)=0 is correct as problem 10 only mentions that the temperatures are fixed. Making the gradients zero means that the ends are insulated. Now we can have a fixed temperature even if flux is non-zero (if flux in is same as flux out). The part that i am confused about is that while solving X equation we will have non-zero solutions for all values of lambda .. so do we solve three general cases according to lambda values. But the solution at the book's back only mentions a single solution !!. | ||
Revision as of 13:12, 5 December 2010
Homework 14 collaboration area
Question Page 560, Problem 11:
Are the boundary conditions for this problem u(0,t)=U1 and u(L,t)=U2 or u'(0,t)=U1 and u'(L,t)=U2? I think it is the u' option, but I'm not sure why?
Answer: The problem says that it is fixed at U1 and U2 for all time. I interpret this as X(0)=U1 and X(L)=U2, and X'(0)=X'(L)=0 since they are not changing at those points. Apply these to the X equation after you separate your variables. The T equation will come out the same as before.
RESPONSE: I don't think that X'(0)=X'(L)=0 is correct as problem 10 only mentions that the temperatures are fixed. Making the gradients zero means that the ends are insulated. Now we can have a fixed temperature even if flux is non-zero (if flux in is same as flux out). The part that i am confused about is that while solving X equation we will have non-zero solutions for all values of lambda .. so do we solve three general cases according to lambda values. But the solution at the book's back only mentions a single solution !!.
Question Page 585, Prob 6:
Can anyone provide some direction on how to start this problem? I'm not really sure how to get started on it.
Question Page 568, Prob 2:
What are the limits of integration for A(p) and B(p) in this problem. I think it is -infinity to infinity, but I'm not sure if this is correct.
Answer: see page 508 for a Fourier Integral refresher. You are right that it is -inf to inf.
