Stokes first problem: hydrodynamic separation of variables

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Explores the Fourier transform application to LTI systems, including frequency response, convolution, differentiation, and solving differential equations.

Numerical Methods: Boundary Value Problems

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

Fourier Transformation: Solving Differential Equations

Explores using Fourier transformation to solve differential equations, focusing on a specific example and deriving the solution formula step by step.

Laplace Transform: Solving Differential Equations

Discusses the application of the Laplace transform to solve differential equations and explores its properties and examples.

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.

Signals, Instruments, and Systems: System Properties and Transforms

Introduces system properties, Laplace Transform, and analog filters for signal analysis.

Fourier transforms: Light-matter interaction

Explores Fourier and Laplace transforms in materials science, focusing on light-matter interaction, diffraction patterns, and crystal properties.

Fourier Series and Equations

Covers Fourier series, periodic functions, and Fourier transforms.

Laplace Transform: Basics and Properties

Covers the basics of the Laplace transform, properties, and applications to LTI systems, including transfer function and frequency response.

Harmonic Analysis: Schwerte Functions

Explores Schwerte functions in harmonic analysis, emphasizing compact support and function convergence.