Fourier Transform: Properties and Applications

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Covers the Sturm-Liouville problem, differential equations, and Fourier transforms for solving equations with specific conditions.

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

Covers mathematical concepts from number theory to probability and statistics.

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

Covers the properties and applications of the Laplace transform in solving differential equations.

Covers numerical methods for solving boundary value problems using Crank-Nicolson and FFT.

Introduces Partial Fraction Expansion as a valuable tool for analyzing stable LTI systems.

Covers Laplace Transform, Fourier Transforms, transfer functions, LTI systems, and Region of Convergence properties.

Covers Fourier series, periodic functions, and Fourier transforms.

Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.