Concept

Residue (complex analysis)

Related lectures (32)

Analytic Continuation: Residue Theorem

Covers the concept of analytic continuation and the application of the Residue Theorem to solve for functions.

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Laplace Transform: Analytic Continuation

Covers the Laplace transform, its properties, and the concept of analytic continuation.

Residue Theorem: Calculating Integrals on Closed Curves

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

Residues and Singularities

Covers the calculation of residues, types of singularities, and applications of the residue theorem in complex analysis.

Complex Analysis: Laurent Series

Explores Laurent series in complex analysis, emphasizing singularities, residues, and the Cauchy theorem.

Laurent Series and Residue Theorem: Complex Analysis Concepts

Discusses Laurent series and the residue theorem in complex analysis, providing examples and applications for evaluating complex integrals.

Inverse Laplace Transform: Examples

Covers the inverse Laplace transform with examples and methods for solving complex roots.

Residues Theorem Applications

Explores applications of the residues theorem in various scenarios, with a focus on Laurent series development.

Unclosed Curves Integrals

Covers the calculation of integrals over unclosed curves, focusing on essential singularities and residue calculation.

Trigonometric Integrals: Residues Method

Covers the calculation of integrals using the residues method and discusses singularities, poles, and examples.

Residues Method: Generalized Integrals

Covers the calculation of generalized integrals using the residues method and provides examples for better understanding.

Essential Singularity and Residue Calculation

Explores essential singularities and residue calculation in complex analysis, emphasizing the significance of specific coefficients and the validity of integrals.

Inverse Z Transform: Properties and Linear Systems

Explores the inverse Z transform, properties of linear systems, and signal decomposition.

Generalized Integral and Main Value

Covers the concept of the generalized integral and main value, including singularities, principal value at infinity, and residues.

Fourier Transform: Residue Method

Covers the calculation of Fourier transforms using the residue method and applications in various scenarios.

Mellin Transform: Residue Method

Covers the calculation of Mellin transforms using the residue method and provides examples of its application.

Underdamped Response of 2nd Order System

Explores the underdamped response of a 2nd order system and how damping affects oscillation frequency and decay.

Passivity in Mass-Spring Systems

Explores passivity in mass-spring systems, calculating transfer functions and ensuring system passivity through feedback assembly.

Residues Theorem

Explores the Residues Theorem and the classification of holomorphic functions.