Lectures related to Stochastic Differential Equations: Examples and Relations

Maximum Entropy Principle: Stochastic Differential Equations

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.

Evolution of Partial Differential Equations

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

Numerical Methods: Boundary Value Problems

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

Fourier Transform and Partial Differential Equations

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

Diffusion: Macroscopic View

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

Partial Differential Equations

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

Laplace Poisson Equation

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

Heat and Wave Equations: Analysis IV

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

Complex Analysis: Laplace and Fourier Transforms

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

Complex Analysis: Residue Theorem and Fourier Transforms

Discusses complex analysis, focusing on the residue theorem and Fourier transforms, with practical exercises and applications in solving differential equations.

Partial Differential Equations: Heat Equation in R

Explores solving differential equations with periodic data using Fourier series and delves into the heat equation in R.

The Black-Scholes-Merton Model

Covers the Black-Scholes-Merton model, dynamics, self-financing strategies, and the PDE.

Introduction to Numerical Methods for PDEs

Covers the numerical approximation of PDEs and examples of nonlinear behavior.

Numerical Approximation of PDEs

Covers the numerical approximation of PDEs, including Poisson and heat equations, transport phenomena, and incompressible limits.

Biomechanics Modeling: Musculoskeletal System

Explores biomechanical modeling of the musculoskeletal system using differential equations and finite element modeling.

Partial Differential Equations: Equations and Solutions

Explores partial differential equations, focusing on chapter 6 equations and their solutions through Fourier series and variable separation methods.

Differential Equations: Speed Variation Analysis

Covers the analysis of speed variation using differential equations and small time intervals.

Nonlinear PDE Models with Stochastic Fractional Perturbation

Explores nonlinear PDE models with stochastic fractional perturbation, focusing on regularity identification and space-time noise interpretation.

Automorphic Kernels: Heat Equation Solutions

Explores automorphic kernels and their role in solving the heat equation.