Lectures related to Partial Differential Equations: Basics

Diffusion: Macroscopic View

Explores diffusion from a macroscopic perspective, emphasizing the derivation of the diffusion equation through mass conservation and fixed flux law.

Fourier Analysis and PDEs

Explores Fourier analysis, PDEs, historical context, heat equation, Laplace equation, and periodic boundary conditions.

Boundary Conditions and Basis Decomposition

Explores boundary conditions, basis functions, and PDE solutions using Fourier and Bessel series.

Distribution & Interpolation Spaces

Explores distribution and interpolation spaces, differential operators, Fourier transform, Schwartz space, fundamental solutions, Farrier transform, and uniform continuity.

Partial Differential Equations

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

Introduction to Partial Differential Equations

Covers the basics of Partial Differential Equations, focusing on heat transfer modeling and numerical solution methods.

Fourier Transform and Partial Differential Equations

Explores the application of Fourier transform to PDEs and boundary conditions.

Two Phase Flow and Heat Transfer

Covers the fundamentals of two-phase flow and heat transfer phenomena.

Heat Transfer Applications

Explores the applications of the Fourier equation in heat transfer phenomena.

Parabolic Heat Equation: Modeling and Simulation

Explores the parabolic heat equation evolution and numerical solution methods.

Numerical Methods for Boundary Value Problems

Covers numerical methods for solving boundary value problems using finite difference, FFT, and finite element methods.

Partial Differential Equations: Laplace Equation

Explains the Laplace equation in 2D with mixed boundary conditions.

Heat Equation in 1D: Chapter 12

Explores the heat equation in 1D, emphasizing conservation of thermal energy and numerical solution methods.

Time-dependent Diffusion: Fourier Trick

Explores the Fourier Trick for time-dependent diffusion problems in a Cartesian system.

Introduction to PDES

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

Linear Partial Differential Equations

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

Fourier Series and PDE Solving

Covers the solving of PDEs using Fourier series and boundary conditions of Neumann and Dirichlet type.

Quantum Mechanics: Power Series Solutions

Explores power series solutions in quantum mechanics for differential equations and energy quantization.

Numerical Methods: Boundary Value Problems

Explores boundary value problems, finite difference method, and Joule heating examples in 1D.

Numerical Approximation of Partial Differential Equations

Explores numerical methods for solving partial differential equations computationally, emphasizing their importance in predicting various phenomena.