Introduction to PDES

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Related lectures (28)

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Boundary Conditions in Harmonic Functions

Explains harmonic functions and their boundary conditions, including Dirichlet and Robin 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.

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.

Uniqueness Results for Poisson Equation

Explores uniqueness results for the Poisson equation and harmonic functions with different boundary conditions.

Linear Partial Differential Equations

Explores linear partial differential equations, elliptic PDEs, Laplace equation, boundary conditions, and classical solutions.

Poisson Problem: Fourier Transform Approach

Explores solving the Poisson problem using Fourier transform, discussing source terms, boundary conditions, and solution uniqueness.

Maximum Principle in Harmonic Functions

Explores the maximum principle in harmonic functions and its implications for uniqueness and bounds on solutions.

Partial Differential Equations

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