Fourier Transform: Analysis Tools

Related lectures (29)

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Covers the Fourier transform in Analysis IV, discussing Fourier series and solutions for various problems.

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

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

Covers Fourier series, analysis, the heat equation, Gibbs phenomenon, and Fourier transform properties.

Explores solving the Poisson problem using Fourier transform, discussing source terms, boundary conditions, and solution uniqueness.

Explores Fourier series, DFT, FFT, and their applications in signal processing and spectroscopy.

Explores Fourier series coefficients, periodicity, and series relations.

Discusses Laplace and Fourier transformations, focusing on their inversion formulas and applications in solving differential equations.

Covers the properties and applications of the Fourier transform and its relation to Heisenberg's uncertainty principle.

Explores the Central Limit Theorem, convergence in law, characteristic functions, and moment problems in probability theory.