← GATE Mathematics guide GATE Mathematics · Section 4

Complex Analysis

Analytic functions through to residues and conformal maps — directly covered.

Books that cover Section 4

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Complex Analysis

M.A. & M.Sc. Mathematics · Dr. H.K. Pathak

Covers: The full section — analytic & harmonic functions, Cauchy’s theorem & formula, Taylor/Laurent series, the residue theorem with real-integral applications, Rouché & the argument principle, and conformal & Möbius maps.

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Full syllabus — Section 4

Functions of a complex variable: continuity, differentiability, analytic and harmonic functions
Complex integration: Cauchy’s integral theorem & formula; Liouville’s theorem; maximum modulus principle; Morera’s theorem
Zeros and singularities; power series, radius of convergence; Taylor & Laurent series
Residue theorem and applications to real integrals; Rouché’s theorem; argument principle; Schwarz lemma; conformal & Möbius transformations

Section 3: Real Analysis Section 5: Ordinary Differential Equations