Complex Analysis: A Geometric and Visual Approach
Abdel Rahman Al-Abdallah *
Brandon University, Manitoba, Canada.
*Author to whom correspondence should be addressed.
Abstract
This book develops classical function theory through a geometric lens. Beginning with the Cauchy–Riemann equations and harmonic functions, it builds the machinery of Laurent series, residues, and contour integration; develops a toolkit for conformal maps, Mobius transformations, and automorphism groups; and culminates with the Riemann Mapping Theorem plus an accessible entry to elliptic functions and complex tori. Lecture-note clarity, worked examples, and concise proofs make it ideal for classroom use and self-study.
Keywords: Complex analysis, analytic functions, Cauchy–Riemann equations, harmonic functions, Laurent series, residue theorem, contour integration, conformal mappings, M¨obius transformations, automorphism groups, riemann mapping theorem, elliptic functions, complex tori