Distribution & Interpolation Spaces

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Distributions & Interpolation Spaces

Covers distributions, interpolation spaces, convergence, and the concept of dual spaces.

Finite element methods

Covers finite element methods for solving diffusion problems in porous media, including meshing, interpolation, and weighted residuals.

Inverse Monotonicity: Stability and Convergence

Explores inverse monotonicity in numerical methods for differential equations, emphasizing stability and convergence criteria.

Linear Partial Differential Equations

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

Numerical Methods: Boundary Value Problems

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

Heterogeneous Reactions: Transport Effects

Explores transport effects in heterogeneous catalysis, including molecular diffusion and Knudsen diffusion in different types of pores.

Introduction to PDES

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

Rayleigh Taylor: Normal Mode Expansion

Explores normal mode expansion, Laplace equation solution, and dispersion relation analysis in Rayleigh Taylor instability.

Fourier Transform: Concepts and Applications

Covers the Fourier transform, its properties, applications in signal processing, and differential equations, emphasizing the concept of derivatives becoming multiplications in the frequency domain.

Time-dependent Diffusion: Fourier Trick

Explores the Fourier Trick for time-dependent diffusion problems in a Cartesian system.