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Jun11-05, 08:27 AM
Sci Advisor
HW Helper
P: 1,593
We have a LaTex-enabled compiler here. You just write the LaTex commands in the post and the compiler formats it. For example:

[tex]\text{DE:}\quad u_t-u_{xx}=tSin(x) \qquad 0\leq x\leq \pi[/tex]

[tex]\text{BC:}\quad u(0,t)=0 \qquad u(\pi,t)=0[/tex]

[tex]\text{IC:}\quad u(x,0)=0[/tex]

See how nice that looks. You can just double-click on any of the equations in here and a window will pop-up with the latex commands or just go to the Physics forum and see the "introducing LaTex" thread. Now, the equation above is just a rod with an internal heat source that eventually develops into a sine wave. This one is easily solved using Duhamel's principle. It looks like:

Edit: Suppose the heat source is a sine wave. It just gets bigger (hotter) and bigger with time.
Attached Thumbnails
heat equation.JPG