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The bookUnit 2 · Singularities and Residues35 / 83

Residue theorem and standard contour integrals

Why this is asked: Five standard contour patterns cover almost every exam integral. Know which contour goes with which integrand, and remember that a semicircular indentation contributes iπ·Res, not 2πi·Res.

Residue theorem — the five standard patterns

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Computing residues without expanding the seriesinteractive

Simple poles, higher-order poles and the check that catches arithmetic slips.

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For an integer k, consider the contour integral Ik=z=1I_{k} = \int_{|z|=1} eᶻ/zᵏ dz. Which of the following statements are true?

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Open this in the full syllabus view · Unit 2