Introductory PDE (diffusion equation)

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Homework Statement

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

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 {4x^2}{e^{-x^2}}, 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.

 

[compliant]

bump.