Fourier Transform and Residue Calculus

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Related lectures (29)

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Fundamental Theorem of Algebra

Covers the Fundamental Theorem of Algebra, complex sequences, convergence, and continuity of functions.

Laplace Transform: Properties and Applications

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

Fourier Transform: Schwartz Space

Covers the Fourier transform on Schwartz space and its properties, including continuity and linearity, as well as the density of smooth compactly supported functions.

Julia Sets and Polynomial Roots

Explores Julia Sets, polynomial roots, Newton's method, and critical points in complex functions.

Fourier Series: Convergence and Coefficients

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

Fourier Series and Analysis

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

Green Functions and Complex Analysis

Covers EM fields of moving charged particles and Green functions.

Fourier Transform: Properties and Convolution

Covers the properties and convolution of the Fourier transform.

Properties of Fourier and inverse Fourier transforms

Explores the properties of Fourier and inverse Fourier transforms, analyzing finite wave trains, Gaussian functions, and 3D space transformations.