Lectures related to Green's identities

Divergence Theorem: Green Identities in R²

Explores the divergence theorem and corollaries related to Green identities in the plane, demonstrating their application through examples.

Green Theorems: Divergence Theorem and Identities of Green

Explores the application of Green theorems in 2D and 3D spaces.

Green's Theorem: Surface Integrals

Explores Green's Theorem applied to surface integrals, emphasizing regular surfaces and coordinate transformations.

Green's Functions in Laplace Equations

Covers the concept of Green's functions in Laplace equations and their solution construction process.

Notations and Identities: Recap of Prerequisite Concepts

Covers conventions, demonstrations, factorials, binomial expansions, and Pascal's triangle in mathematical calculations.

Dirichlet Problem for Laplace Equation

Explores the Dirichlet problem for the Laplace equation and Green's function.

Mathematical Methods: Oscillations and Energy Transfer

Discusses oscillations, energy transfer, and the Green function in physics.

Vector Calculus: Green's Theorem

Explores Green's theorem, vector field curl, Ampère's law, and magnetic field modeling.

Surface Orientation Analysis

Discusses surface orientation analysis, normal vectors, and Green's identities application.

Linear Hatching Systems: Unique Solutions and Norm Introduction

Explores linear hatching systems, unique solutions, norms, and fixed points in linear systems.

Green Function and Laplacian Formula

Covers the concept of Green function and Laplacian formulas in mathematics.

Dirichlet Problem on the Ball

Covers the Dirichlet problem on the ball and the solution to the Dirichlet problem on the half plane.

Electrostatics and Green's Functions: Mathematical Methods

Discusses electrostatics, Green's functions, and the application of complex analysis in deriving potentials.

Green Functions: Theory and Applications

Explores the theory and applications of Green functions in classical electrodynamics, emphasizing the importance of choosing the right function based on boundary conditions.

Green Theorems: Gauss Application

Covers the Green and Gauss theorems, focusing on their applications in vector calculus.

Point Estimation in Statistics

Covers the concept of point estimation in statistics, focusing on methods to estimate unknown parameters from a given sample.

Stokes Theorem

Covers the Stokes theorem, extending the Green theorem to surfaces in R3 and explaining its application.

Powers: Whole Numbers

Covers the definition and properties of whole number powers, including examples and proofs.

Group Theory: Special Cases

Covers special cases in group theory, focusing on group actions and functors.

General Existence Results for PDEs

Covers the general existence result for the Laplace-Dirichlet problem and the properties of the Newtonian potential.