Unbounded and Bounded Systems: Fourier Methods

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Poisson Problem: Periodic Boundary Conditions

Explores the Poisson problem with periodic boundary conditions and the application of Fourier series in mathematical modeling.

Fourier Transform: Analysis IV

Covers the Fourier transform in Analysis IV, discussing Fourier series and solutions for various problems.

Wave Propagation: General Solutions

Explores the general solutions for wave propagation and Fourier transforms in periodic functions.

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.

Partial Differential Equations: Reflow and Light Propagation

Explores PDEs through reflow of polymer film and light propagation in optical fibers.

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: Concepts and Applications

Covers the Fourier transform, its properties, and applications in signal processing and differential equations, demonstrating its importance in mathematical analysis.

Transient Regime: Heat Transfer

Explores the transient regime in heat transfer, solidification, boundary conditions, and heat flux density.

Complex Integration: Fourier Transform Techniques

Discusses complex integration techniques for calculating Fourier transforms and introduces the Laplace transform's applications.