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.
Author(s)
Abdel Rahman Al-Abdallah
Brandon University, Manitoba, Canada.
ISBN 978-81-992493-2-5 (Print)
ISBN 978-81-992493-5-6 (eBook)
DOI: https://doi.org/10.9734/bpi/mono/978-81-992493-2-5
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.