Complex Analysis
Prof. P. N. Agarwal
Learn analytic functions and complex integration with Prof. Agarwal's Complex Analysis course. Explore key theorems and applications.
More resources on Analytic Functions
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.
A First Course in Complex Analysis
Open textbook (CC BY 4.0, version 1.6) for a one-semester undergraduate course. It moves from complex differentiability and Cauchy's theorem to power series and the Residue Theorem, with over 250 exercises and SageMath prompts. Best free rigorous entry-level text; gives beginners a no-cost alternative to Conway (graduate level). A free PDF is available.
Functions of One Complex Variable
Conway's graduate text in the Springer GTM series, a standard first-year course reference. It proves the core theory rigorously, from analytic functions and Cauchy's theorem through the Riemann mapping theorem, Runge's theorem, analytic continuation, and harmonic and entire functions.