Residue (complex analysis)

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Related lectures (32)

Green Functions and Electrostatics

Explores Green functions, complex analysis, and electrostatics, including EM waves and residue theorem.

Residue Theorem: Applications in Complex Analysis

Discusses the residue theorem and its applications in complex analysis, including integral calculations and Laurent series.

Laplace Transform Basics

Covers the Laplace transform basics, including examples of complex-valued poles and its application to LTI systems.

Analyzing Poles and Residues

Covers the analysis of poles and residues in complex functions, focusing on the calculation of singularities, poles, and residues.

Proof of Explicit Formula

Covers the proof of the explicit formula for the non-vanishing of the zeta function at the 1-line.

Residue Calculation and Singularities Classification

Covers the calculation of residues and the classification of singularities in complex functions.

Complex Analysis: Cauchy Integral Formula

Explores the Cauchy integral formula in complex analysis and its applications in evaluating complex integrals.

Complex Analysis: Laurent Series and Residue Theorem

Discusses Laurent series, residue theorem, and their applications in complex analysis.

Convergence and Poles: Analyzing Complex Functions

Covers the analysis of complex functions, focusing on convergence and poles.

Taylor Polynomials: Special Cases

Explores Taylor polynomials, odd orders, simplification, residues, and special cases of zero polynomials.

Complex Analysis: Residue Theorem and Fourier Transforms

Discusses complex analysis, focusing on the residue theorem and Fourier transforms, with practical exercises and applications in solving differential equations.

Residual Theorem: Cauchy

Covers the residual theorem from Cauchy, focusing on simple closed curves and holomorphic functions.

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