Introductory PDE (diffusion equation)

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Homework Statement



[tex]u_t = -{{u_{x}}_{x}}[/tex]
[tex]u(x,0) = e^{-x^2}[/tex]

Homework Equations





The Attempt at a Solution


The initial state is a bell curve centred at x=0. The second partial derivative of u at t=0 is [tex]{4x^2}{e^{-x^2}}[/tex], which is a Gaussian function, which means nothing to me other than its bell-curved shape.

The solution is http://www.orcca.on.ca/~reid/Courses//AMath315/Fall2009/Solutions/Assign1-Fab.pdf" (the top graph), but I just want to know how on earth he (my prof who wrote up said solutions) came up that graph for time t + delta t, and what on earth he means by whatever it is he wrote down there.[tex]
 
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bump.
 

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