This math module will focus on elliptical and parabolic PDEs associated with transport phenomenon problems in biomedical engineering. We will visit four PDE concepts: Separation of variables, integral transform solutions, superposition principles, and numerical approximations using finite-difference schemes. Topics include: 2D and 3D anisotropic Laplace's, Poisson's, and the heat equations in different coordinate systems, Fourier and Laplace transform solutions, 2D ADI methods, Green's functions, and the method of images. Prior exposure to linear algebra (BE 601 equivalent), ODEs (BE 602 or MA 226 equivalent), Fourier series, Fourier and Laplace transforms (BE 401 equivalent), and working knowledge of a programming language (Matlab, Python, etc.) is highly recommended.

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