Semestre 2022-2
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Ecuaciones Diferenciales Parciales
Posgrado en Ciencias Matemáticas (UNAM)
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Online classes
Introduction and general information
Section I: First order PDEs
Transport equation Method of characteristics Quasilinear first order PDEs Loss of regularity Multi-d and fully nonlinear PDEs
Introduction to scalar conservation laws Rankine-Hugoniot conditions Entropy conditions
Section II: Laplace's equation
Laplace and Poisson equations Fundamental solution of Laplace's equation Solving Poisson's equation Mean-value formulas
Properties of harmonic functions Properties of harmonic functions II Green's function Exterior domains. Laplace-Dirichlet Problem
Section III: Heat (or diffusion) equation
Derivation of heat equation and fundamental solution Cauchy problem and Fourier Transform Nonhomogeneous problem
Mean-value formula and maximum principle Properties and uniqueness of solutions Energy methods and separation of variables
Separation of variables and IBVP Viscous Burgers equation
Section IV: Wave equation
Wave equation and d'Alembert's formula A reflection method. Spherical means Kirchhoff's and Poisson's formulas
Solution for any dimensions Nonhomogeneous problem. Energy methods Separation of variables Second Order Linear PDEs
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Tareas
Tarea 3: Heat (or diffusion) equation
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