Fourier Analysis: Applications and Inversion Formula

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

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

Explores control of dynamic systems, impulse response, Laplace transform, and Fourier transform for solving differential equations.

Provides an overview of Fourier and Laplace transforms, their properties, and applications in signal analysis.

Explores using Fourier transformation to solve differential equations, focusing on a specific example and deriving the solution formula step by step.

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

Covers the Dirichlet theorem and complex Fourier coefficients for periodic functions.

Explores the Dirac delta, Fourier integral, and Fourier transform applications in solving PDE problems.

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

Explores Fourier series convergence and coefficient calculations through examples and derivations.