Stochastic Differential Equations: Examples and Relations

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Explores the application of randomness in physical models, focusing on Brownian motion and diffusion.

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

Explores the evolution of PDEs, focusing on heat and wave equations in 1D, uniqueness of solutions, and the d'Alembert formula.

Covers numerical methods for solving boundary value problems, including applications with the Fast Fourier transform (FFT) and de-noising data.

Explores the application of Fourier transform to PDEs and boundary conditions.

Explores diffusion from a macroscopic perspective, emphasizing the derivation of the diffusion equation through mass conservation and fixed flux law.

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

Covers the Laplace and Poisson equations, the heat equation, and the wave equation in physics.

Covers the study of the heat and wave equations, including the process of separating variables to find solutions.

Discusses complex analysis, focusing on Laplace transforms, Fourier series, and the heat equation's solutions and uniqueness.