Fourier Analysis: Inversion Formula and Periodic Functions

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Signal Representations

Covers the properties of signal/data representations using Fourier transformations and matrices.

Fourier Transform and Schwartz Space

Explores the Fourier transform, Schwartz space, and Riemann-Lebesgue lemma in quantum physics.

Fourier Analysis: Applications and Inversion Formula

Explores Fourier analysis applications and the inversion formula in the context of periodicity and continuous functions.

Wave Propagation: General Solutions

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

Fourier transforms: Light-matter interaction

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

Fourier Analysis: Inversion Formula

Explores the Fourier inversion formula and the importance of the integral on the half-circle being zero for the method to work.

Complex Integration: Fourier Transform Techniques

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

Fourier Analysis and PDEs

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

Fourier Transform: Concepts and Applications

Covers the Fourier transform, its properties, applications in signal processing, and differential equations, emphasizing the concept of derivatives becoming multiplications in the frequency domain.

Ewald Summation: Long-Range Interaction and Self-Interaction Correction

Explains Ewald summation, self-interaction correction, and short-range interaction calculations.