Time-dependent Diffusion: Fourier Trick

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Fourier Series and PDE Solving

Covers the solving of PDEs using Fourier series and boundary conditions of Neumann and Dirichlet type.

Partial Differential Equations

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

Introduction to PDES

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

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Trigonometric Functions: Right Triangle

Introduces trigonometric functions in right triangles, exploring angles, ratios, and special values.

Partial Differential Equations: Separation of Variables

Explores the method of separation of variables for solving partial differential equations with boundary conditions and discusses convergence properties of functions in different spaces.

Finite Difference Method: Approximating Derivatives and Equations

Introduces the finite difference method for approximating derivatives and solving differential equations in practical applications.

Heterogeneous Reactions: Transport Effects

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

Partial Differential Equations: Laplace Equation

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

Inverse Monotonicity: Stability and Convergence

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