Lectures related to Fourier Analysis: Inversion Formula and Periodic Functions

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

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.

Determinantal Point Processes and Extrapolation

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

Fourier Series and Equations

Covers Fourier series, periodic functions, and Fourier transforms.

Scaling & Renormalization in Statistical Mechanics

Explores scaling and renormalization in statistical mechanics, emphasizing critical points and invariant properties.

Wavelet Design: Fourier Transform

Covers the design of wavelets using Fourier transform and procedures for selecting wavelet functions.

Fourier Analysis: Stokes Theorem

Explores the application of Stokes' theorem to surfaces and vector spaces in Fourier analysis.

Fourier Analysis III

Covers Fourier coefficients, periodic functions, Fourier transform, and convolution product applications in signal processing.

Signal Representation: Fourier Transforms

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

Inverse Fourier Transform: Verification and Properties

Focuses on the inverse Fourier transform, verification, and properties.

Fourier Transform: Inversion Formula

Covers the Fourier transform inversion formula with examples and exercises for verification.

Fourier Optics: Wavefront Analysis

Explores Fourier optics, diffraction principles, Fourier analysis, and the application of Fourier transform in optics.