Lectures related to Heat Equation: Separation of Variables

Fourier Analysis and PDEs

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

Heat Equation: Modeling and Numerical Methods

Covers the heat equation, its physical interpretation, and numerical methods for solving it.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Heat Equation: Diffusion

Covers the heat equation for diffusion and conservation of thermal energy.

Optimal Transport: Gradient Flows

Explores optimal transport, gradient flows, the implicit Euler scheme, and the heat equation in the context of Dirichlet energy functional.

Maximum Principle in Heat Equation

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

Heat Equation in 1D: Chapter 12

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

Optimal Transport: In-Depth Evaluation

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

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Thermal Diffusion: Basics and Applications

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

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

Numerical Methods: Boundary Value Problems

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

Diffusion: Macroscopic View

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

Heat Equation: Core and Solutions

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

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Heat Integration: Lecture 10

Covers the evaluation of projects, project slots, heat integration, weak solutions, and projection of solutions.

Diffusion Equation

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

Heat Equation: Fourier Series

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

Heat Exchangers: Fundamentals and Applications

Explores the fundamentals of heat exchangers, including conduction, convection, and temperature profiles, with practical examples.

Differential Equations: General Solutions and Methods

Covers solving linear inhomogeneous differential equations and finding their general solutions using the method of variation of constants.