Elliptic Partial Differential Equations

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Theoretical Study of Elliptic Partial Differential Equations

Covers the theoretical study of Elliptic Partial Differential Equations, including classical and weak solutions.

Laplace Poisson Equation

Covers the Laplace and Poisson equations, the heat equation, and the wave equation in physics.

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.

Poisson & Laplace Equations: Understanding Electrostatics

Explores the derivation of a potential function without knowing the charge distribution and its practical implications in analyzing electrostatic problems.

Fundamental Solutions

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

Linear Partial Differential Equations

Explores linear partial differential equations, elliptic PDEs, Laplace equation, boundary conditions, and classical solutions.

Maximum Principle in Harmonic Functions

Explores the maximum principle in harmonic functions and its implications for uniqueness and bounds on solutions.

Introduction to PDES

Covers harmonic functions, Laplacian operator, Dirichlet and Robin problems, and sub-harmonic functions in Partial Differential Equations.

Partial Differential Equations: Basics and Classification

Introduces the basics and classification of partial differential equations, including notation, definitions, and examples.

Finite Difference Methods: Linear Systems and Band Matrices

Covers the application of finite difference methods to solve partial differential equations.