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This course presents practical methods for solving partial differential equations (PDEs). The course covers solutions of hyperbolic, parabolic, and elliptic equations in two or more independent variables. Topics include Fourier series, separation of variables, existence and uniqueness theory for general higher-order equations, eigenfunction expansions, numerical methods, Green’s functions, and transform methods. MATLAB, a high-level computing language, is used in the course to complement the analytical approach and to motivate numerical methods.