Lectures in course MATH-305: Introduction to partial differential equations

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

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

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

Covers the theoretical study of Elliptic Partial Differential Equations, including electrostatics and advection-diffusion-reaction equations.

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

Explores sub/super harmonic functions and their applications in a theoretical context.

Explains harmonic functions and their boundary conditions, including Dirichlet and Robin conditions.

Covers the properties of harmonic functions and the concept of mollification.

Explores uniqueness results for the Poisson equation and harmonic functions with different boundary conditions.

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

Explores uniqueness results and the fundamental solution of the Laplace equation.

Explores fundamental solutions of the Laplace equation and their physical interpretation.

Explores fundamental solutions, Green's formula, distributions, and convergence in Laplace equation.

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

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

Covers Green's representation formula, fundamental solutions, and distribution properties.

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

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

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

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