residues

What problem does it solve?

This Skill provides strategies and tools for calculating residues of complex functions, classifying singularities, and applying the Residue Theorem for contour integration.

Core Features & Use Cases

• Residue Computation: Calculate residues for simple poles, poles of higher order, and essential singularities.
• Singularity Classification: Identify the type and order of singularities of a complex function at a given point.
• Residue Theorem Application: Evaluate contour integrals using the sum of residues inside the contour.
• Use Case: You need to evaluate the integral of a complex function around a closed curve. This Skill can help you find the poles inside the curve, compute their residues, and apply the Residue Theorem to find the integral's value.

Quick Start

Use the residues skill to compute the residue of the function 1/((z-1)*(z-2)) at z=1.