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Description: |
Physical phenomena in a wide range of areas such as fluid and solid mechanics, electromagnetism, quantum mechanics, chemical diffusion, and acoustics are governed by Partial Differential Equations (PDEs). In this course, you will learn how to solve a variety of BVPs, each of which is defined by a PDE, boundary conditions, and possibly initial conditions. We will cover the classical PDEs of mathematical physics: 1) diffusion equation, 2) Laplace equations, 3) wave equation. You will learn different techniques to solve these equations. Topics include separation of variables, Fourier analysis, Sturm-Liouville theory, spherical coordinates and Legendre’s equation, cylindrical coordinates and Bessel’s equation, method of characteristics, and Green's functions. You will also learn the basics of how to discretize linear and nonlinear PDEs and solve them numerically. Emphasis will be on physical understanding of the governing equations and the resulting solutions. You will learn to use software and write code (Python, Matlab, Mathematica) to solve PDEs and visualize the solutions. Prior knowledge of any of these languages/software, although helpful, is not required. |