Linear Partial Differential Equations

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Linear PDEs of Order 2

Covers linear PDEs of order 2, focusing on elliptic second-order PDEs and boundary conditions.

Boundary Conditions and Basis Decomposition

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

Classification of PDEs: Linear, Semi-linear, Quasi-linear

Explores the classification of PDEs into linear, semi-linear, and quasi-linear types, emphasizing the properties of their solutions.

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 Analysis and PDEs

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

Partial Differential Equations: Laplace Equation

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

Introduction to PDES

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

Parabolic Heat Equation: Modeling and Simulation

Explores the parabolic heat equation evolution and numerical solution methods.