residues

What problem does it solve?

This Skill provides a structured approach to solving problems involving residues in complex analysis, including computation, classification of singularities, and application of the Residue Theorem.

Core Features & Use Cases

• Residue Computation: Calculates residues for simple poles, poles of higher order, and essential singularities.
• Singularity Identification: Helps in classifying singularities (poles, essential, removable).
• Residue Theorem Application: Assists in evaluating contour integrals using the Residue Theorem.
• Use Case: Given a complex function f(z) and a contour C, this skill can compute the residues of f(z) at its poles inside C and then evaluate the contour integral of f(z) along C.

Quick Start

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