Basic concepts for partial equations (PDEs) and associated conditions. Solving PDEs of first-order, the Cauchy problem, and the method of characteristic. Classification of second-order PDEs, and canonical forms. Well-posedness. The one-dimensional wave equation, D'alambert's method. Trigonometric Fourier series, Fourier transform applications to ODEs and PDEs, the method of separation of variables and Sturm-Liouville problem. The heat and wave equations on a finite interval. The Laplace and poisson equation. The maximum principle and properties of harmonic functions.

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