Basic Concepts for Partial Equations (Pdes) and Associated Conditions. Solving Pdes of First Order, the Cauchy Problem, and the Characteristic Curves. 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 Equations. the Maximun Principle and Properties of Harmonic Functions. Introduction to Numerical Methods for Solving Pdes.