Lectures related to Partial Differential Equations: Equations and Solutions

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

Covers heat equations, Fourier transforms, and variable separation methods.

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.

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.

Differential Equations: Speed Variation Analysis

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

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.

Boundary Conditions and Basis Decomposition

Explores boundary conditions, basis functions, and PDE solutions using Fourier and Bessel series.

Properties of Fundamental Solutions: Green's Representation Formula

Covers the properties of fundamental solutions and introduces Green's representation formula for solving partial differential equations.

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.

Maximum Entropy Principle: Stochastic Differential Equations

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

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.

Applications of Fourier Equation

Explores applications of the Fourier equation in different heat transfer scenarios.

Numerical Methods: Boundary Value Problems

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

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.

Numerical Methods for Boundary Value Problems

Covers numerical methods for solving boundary value problems using finite difference, FFT, and finite element methods.

Numerical Analysis: Stability in ODEs

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

Mathematical Methods for Physicists: Differential Equations and Special Functions

Covers solving differential equations and special functions essential for physicists, emphasizing practical problem-solving skills.