Project 6: Fourier Transform for Solving Diffusion Equations

Go through the section 4.5 Fourier Transform of the test book, have a report of the introduction of Fourier Transform for solving diffusion equations. \(u_t = Du_{xx}, \quad \text{for } -\infty < x < \infty, \quad 0 < t,\) with the initial condition \(u(x, 0) = f(x).\) It is assumed that \(f(x)\) is piecewise continuous with \(\lim_{x\rightarrow \pm\infty}f(x) = 0\). Students choose this project should be able to understand the convolution theorem and how to solve the diffusion equation.