PDE solutions using Fourier Transforms

See attached PDF for the compiled LaTex. I would prefer any solution include the Latex Source, however, if you are unable to use LaTex, you may use another format. Exercise 1 Solve, using Fourier Transforms frac{partial^{2}u}{partial x^{2}}+frac{partial^{2}u}{partial y^{2}}=0 for 0 ...continues

Fourier Transform

See attached Using the Fourier transform, solve the diffusion equation in the presence of an advection term:....

Diffusion Equations

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Diffusion Equations : Method of Finite Transforms

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2D Heat Equation

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Green's Function

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Use Laplace and/or Fourier Transform to solve Greens function.

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rational expressions

need help with rational equations and expressions

Analytic solution to the pde

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Heat Equation Problem

Find the solution u(x,t) of the heat equation: ut = 1/2 uxx (a) with initial data u(x,0) = x (b) with initial data u(x,0) = x^2 (c) with initial data u(x,0) = sinx (d) with initial data u(x,0) = 0 x < 0 and u(x,0) = 1 or x >/= 0 I know the solution of the heat equation with given initial data is unique. So if you happe ...continues