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Laurent Series and Residue Calculus (Berkeley handout)

by Nikhil Srivastava · UC Berkeley Department of Mathematics

Short handout stating Laurent's theorem for functions analytic on a punctured disk, defining the principal part, classifying removable singularities, poles and essential singularities by that part, and deriving residue formulas for closed contour integrals.

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Wolfram MathWorld

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

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Complex Variables with Applications (MIT 18.04)

Complex analytic functions and their applications: Cauchy's theorem and integral formula, Taylor and Laurent series, residues for evaluating hard integrals, harmonic functions, conformal maps, two-dimensional fluid flow, and Laplace and Fourier transforms. Provides 14 lecture note files plus problem sets and exams with solutions.

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Analysis of a Complex Kind (video lectures)

Recorded lecture series from Wesleyan University's complex analysis course. Later modules derive Laurent series in annuli, classify isolated singularities, compute residues, and prove the residue theorem, then apply it to evaluating real integrals.

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Math 246A, Notes 4: Singularities of Holomorphic Functions

Graduate lecture notes from UCLA Math 246A treating isolated singularities of holomorphic functions: Laurent expansions on annuli, removable singularities and poles, essential singularities via Casorati-Weierstrass and Picard, meromorphic functions, and the residue theorem.

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Introduction to Complex Analysis

Wesleyan University course on complex analysis covering complex numbers, analytic functions, conformal mappings, Möbius transformations, contour integration, Cauchy's theorem, power and Laurent series, and residues. Learners finish able to evaluate contour integrals and analyze complex-differentiable functions.

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