Lectures related to Heat equation

Maximum Principle in Heat Equation

Explores the maximum principle in the context of the heat equation and the concept of the cylinder.

Maximum Entropy Principle: Stochastic Differential Equations

Explores the application of randomness in physical models, focusing on Brownian motion and diffusion.

Fourier Analysis and PDEs

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

Heat Equation: Separation of Variables

Covers the application of separation of variables method to solve the heat equation.

Optimal Transport: In-Depth Evaluation

Explores optimal transport theory with a focus on heat equations and Wasserstein distance.

Boundary Conditions - 1D Systems

Covers boundary conditions for heat diffusion in 1D systems.

Heat Equation: Core and Solutions

Explores the heat equation core, solutions, and diffusion behavior over time.

Diffusion Equation

Covers the Fourier law, heat equation, Righi-Leduc effect, and related experiments.

Thermal Diffusion: Basics and Applications

Explores thermal diffusion, specific heat, conductivity, and expansion in materials, explaining how energy is transferred between atoms and molecules.

Free Propagation and Heat Equation

Covers free propagation and the heat equation solution, discussing momentum preservation and Fourier multipliers.

Convolution and Fourier Transform

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.

Function Approximations

Covers continuous functions with compact support, density, and approximation, focusing on the heat equation.

Heat Equation: Stationary Distribution

Explores the heat equation, equilibrium equations, heat flux, and harmonic functions in heat distribution.

Numerical Methods: Boundary Value Problems

Covers numerical methods for solving boundary value problems using Crank-Nicolson and FFT.

Heat Equation in 1D: Chapter 12

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

Heat Transmission: Diffusion Equation and Wine Cellar Construction

Explores heat transmission through diffusion equations and wine cellar construction.

2D Conduction: Method of Separation of Variables

Explains the method of separation of variables for 2D conduction problems and the limitations of the electrical analogy.

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

Automorphic Kernels: Heat Equation Solutions

Explores automorphic kernels and their role in solving the heat equation.

Heat Equation: Fourier Series

Explores the heat equation solutions using Fourier series and energy conservation.