Fourier Analysis: Inversion Formula

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

Covers the concept of analytic continuation and the application of the Residue Theorem to solve for functions.

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

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

Introduces Laplace transform, ROC, and LTI systems with transfer functions and frequency response.

Covers the Laplace transform, its properties, and the concept of analytic continuation.

Covers the applications of the Residue theorem in evaluating complex integrals related to real analysis.

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

Explores Fourier inversion formula, periodic functions, and methods comparison.

Covers the concept of Green's functions in Laplace equations and their solution construction process.