Partial Differential Equations: Basics

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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.