Complex Analysis

Academic (University) preparation with worked examples, written practice and independent learning assessments.

Independent university-level study of Complex Analysis. This original curriculum draws on public academic subject descriptions; it is not an official faculty syllabus, university credit, accreditation or an Ivy League qualification. Topics covered: Complex plane; Analytic functions; Cauchy-Riemann equations; Conformal maps. Contour integration; Cauchy theorem; Integral formulas; Derivative estimates. Power series; Analytic continuation; Identity theorem; Maximum principle. Laurent series; Isolated singularities; Residues; Argument principle. Real integral evaluation; Contour choices; Branch cuts; Principal values. Conformal mappings; Mobius transformations; Schwarz lemma; Riemann mapping. Infinite products; Entire functions; Meromorphic functions; Special functions. Harmonic functions; Poisson formula; Boundary problems; Complex methods applications. Projects use safe simulations, public datasets or textual analysis; specialist subject review is required. Includes lessons, supplementary YouTube tutorials, practical exercises, quizzes and free/paid practice tests. Erudex is independent, not affiliated with the source institution or awarding body. Its 80% learning checks are not official grades or university credit. Content requires qualified subject review before use as a complete teaching programme.