Lectures related to Green's Functions in Laplace Equations

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Green's Theorem: Understanding Rotations and Closed Paths

Explores Green's Theorem, rotations, closed paths, and integral signs.

Fundamental Solutions of Laplace Equation

Covers the fundamental solutions of the Laplace equation and introduces distributions.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Curve Integrals: Gauss/Green Theorem

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Magnetostatics: Magnetic Field and Force

Covers magnetic fields, Ampère's law, and magnetic dipoles with examples and illustrations.

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Unclosed Curves Integrals

Covers the calculation of integrals over unclosed curves, focusing on essential singularities and residue calculation.

Green's Function: Theory and Applications

Covers the theory and applications of Green's function in solving differential equations.

Comparison Series and Integrals

Explores the relationship between series and integrals, highlighting convergence criteria and function examples.

Green's Theorem: Applications

Covers the application of Green's Theorem in analyzing vector fields and calculating line integrals.

Generalized Integrals: Definition and Applications

Covers the definition and applications of generalized integrals in advanced analysis, including real functions, differential equations, and multiple integrals.

Transforms of the Place

Explores the intuition behind transforms of the place and addresses audience questions on integral calculations and function choices.

Vector Calculus: Green's Theorem

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

Taylor Series and Definite Integrals

Explores Taylor series for function approximation and properties of definite integrals, including linearity and symmetry.

General Existence Results for PDEs

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

Analytic Continuation: Residue Theorem

Covers the concept of analytic continuation and the application of the Residue Theorem to solve for functions.

Vectorial Fields: Parametrization and Stokes' Theorem

Covers the parametrization of vectorial fields and the application of Stokes' theorem.

Integration of CnR Class Functions

Explains the integration of Taylor series for CnR class functions.

Green's Theorem: Boundary and Normal Vectors

Explores boundaries, normal vectors, and Green's theorem application in transforming integrals.