Heat equation: Separation of variables
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This video is a response to How to solve PDEs via separation of variables + Fourier series. Chris Tisdell UNSW
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All Comments (19)
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What if our boundary conditions u(0,t)= a and u(L,t)= b? Would I end up with the infinite sum (fourier)?
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Yeah Dr. Tisdell--U-r-awsome, great lecture & thanks for being a true teacher. The heck with uncaring teachers.
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@Reyder93 The important point is that the constant must be positive. If we write it as \alpha^2 (with \alpha > 0) then it makes the notation and calculations simpler when solving.
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@DrChrisTisdell Eeeem yeah.I understood....I have had lecture in previous week.My teacher said that in heat equation there must be alfa not alfa square.Is it true????
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Dr Tisdell, you justified the validity of the constant but what is the justification for the characteristic equation?
alquiora 3 weeks ago in playlist Engineering Mathematics 2E (MATH2019)
@alquiora watch?v=xtHGJtsLqbs with the justification starting around 06:40
DrChrisTisdell 3 weeks ago
how we will find Bn??? Bn and bn is the same
Reyder93 2 months ago
@Reyder93 I give the formula for b_n at 46:48.
DrChrisTisdell 2 months ago
one more question....If in initial condition we were given U(x,0)=m(L-x) and my final equation from which we will find bn is Bnsin(nx)
Reyder93 2 months ago
@Reyder93 If you go to my channel and click on the Fourier series playlist then you can find several videos that solve the kinds of question that you mention.
DrChrisTisdell 2 months ago