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How do we solve the folllowing diffusion problem?

$u_t=4u_{xx}$

$u(0,t)=0$

$u(3,t) = 0$

$u(x,0)=\sin(2\pi x/3)-2\sin(\pi x)+7\sin(5\pi x/3)$

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    Are you familiar with the method of separation of variables?2012-11-30
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    This must be a homework. What have you tried? There is just a formula for the general solution involving Fourier coefficients ... and you don't even need to compute those for this problem because you can just read them from the initial distribution!2012-11-30
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    Well, I think this is very straightforward one. If someone says more than use "separation of variables" will be helping more than expected since you doesn't show your work. Maybe is a good idea to make a question over separation of variables method, since I think that is your problem: that you are missing something about it.2012-11-30
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    @elessartelkontar I disagree. I'm teaching a class that does this right now, and if this is a homework problem, then they have probably derived the general solution in class and are not expected to run through separation of variables everytime they solve it.2012-11-30
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    However, if one is supposed to solve a problem is because he knows the subtleties behind solution methods, if not they are not seeing the important part of the method and it is nonsense to solve a problem.2012-11-30
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    The current mathematical eduations are sometimes make us disgusting, as they like to molding some particular types of questions many many times, ignore the innovations to explore many advanced types of questions.2012-11-30
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    I don't really understand what either of the two of you are talking about. It's OK to do calculations in the beginning without fully understanding. This doesn't mean you will never understand the method. Why is it disgusting to a apply a formula that has been fully derived in class? I actually find it disgusting to make students repeatedly re-derive the same thing over and over again. This is the beauty of math. Once you've derived something it is true forever.2012-12-01

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