Shallow Water Waves: Stability and Tsunamis

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Properties of Fourier and inverse Fourier transforms

Explores the properties of Fourier and inverse Fourier transforms, analyzing finite wave trains, Gaussian functions, and 3D space transformations.

Fourier Series: Understanding Coefficients and Periodicity

Explores Fourier series coefficients, periodicity, and series relations.

Fourier Series and Transforms: Introduction and Properties

Covers Fourier series, Fourier transforms, and convolution properties, including linearity and commutativity.

Signal Representation: Fourier Transforms

Covers the representation of signals using Fourier transforms and the properties of signal vectors.

Numerical Methods for Schrödinger Equation

Explores numerical methods for solving the time-dependent Schrödinger equation using grid representation and split-operator algorithms.

Deviation from Bragg Scattering

Discusses scattering deviations from the perfect Bragg condition and introduces the 'excitation error' within a kinematical approximation.

Fourier Transform: Circuit Analysis

Explores the Fourier transform applied to circuit analysis and its properties.

Wave Patterns and Spectral Analysis

Explores wave patterns, Fourier transforms, group velocity, and Gaussian spectra in hydrodynamics.

Reciprocal lattice: Shape effects

Explains how sample geometry affects the size and shape of reciprocal lattice nodes in multiple beam scattering.

Solving unbounded PDE's using Fourier Transforms and Convolution: Obtaining the d'Alembert solution of the wave equation

Explores elementary properties of Fourier Transforms, convolution, Parseval's Theorem, and the d'Alembert solution of the wave equation using Fourier Transforms and convolution.