Heat Equation: Basics and Stability Estimates

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Heat Equation in 1D: Chapter 12

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

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.

Thermal Circuits: Overall Heat Transfer Coefficient

Explores thermal circuits and the overall heat transfer coefficient in the context of heat conduction.

Fourier Transform and Partial Differential Equations

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

Approximation to Boltzmann Equation

Covers the approximation treatments of the Boltzmann Equation for photons, phonons, and electrons, exploring diffusion and ballistic-diffuse approaches.

Partial Differential Equations

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

The Finite Volume Method

Covers the Finite Volume Method for numerical flow simulation, including conservation equations, discretization methods, and boundary conditions.

Heat Equation: Modeling and Numerical Methods

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

Diffusion in Concentration Coordinates

Explores diffusion in concentration coordinates and boundary conditions in different systems.