Density Results in Sobolev Spaces

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Fundamental Solutions

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Extension Theorems: Sobolev Spaces and Poincaré Inequality

Covers extension theorems in Sobolev spaces and Poincaré inequality, emphasizing the importance of understanding these concepts in partial differential equations.

Partial Differential Equations and Hessians

Covers partial differential equations, Hessians, and the Implicit Function Theorem, with a focus on exam question resolution.

Numerical Analysis: Implicit Schemes

Covers implicit schemes in numerical analysis for solving partial differential equations.

Partial Differential Equations

Covers the basics of Partial Differential Equations, including the Laplace equation, heat equation, and wave equation.

Properties of Fundamental Solutions: Green's Representation Formula

Covers the properties of fundamental solutions and introduces Green's representation formula for solving partial differential equations.

Variational Methods in Mechanics

Covers variational methods in mechanics, focusing on the Ritz-Galerkin method.

Classification of PDEs: Linear, Semi-linear, Quasi-linear

Explores the classification of PDEs into linear, semi-linear, and quasi-linear types, emphasizing the properties of their solutions.

Numerical Methods: Boundary Value Problems

Covers numerical methods for solving boundary value problems, including applications with the Fast Fourier transform (FFT) and de-noising data.

Elliptic Partial Differential Equations

Covers the model problem of elliptic PDEs with weak formulation and classical solutions.