Table of Contents

One Basic Theory.- I Complex Numbers and Functions.- II Power Series.- III Cauchy’s Theorem, First Part.- IV Winding Numbers and Cauchy’s Theorem.- V Applications of Cauchy’s integral Formula.- VI Calculus of Residues.- VII Conformal Mappings.- VIII Harmonic Functions.- Two Geometric Function Theory.- IX Schwarz Reflection.- X The Riemann Mapping Theorem.- XI Analytic Continuation Along Curves.- Three Various Analytic Topics.- XII Applications of the Maximum Modulus Principle and Jensen’s Formula.- XIII Entire and Meromorphic Functions.- XIV Elliptic Functions.- XV The Gamma and Zeta Functions.- XVI The Prime Number Theorem.- §1. Summation by Parts and Non-Absolute Convergence.- §2. Difference Equations.- §3. Analytic Differential Equations.- §4. Fixed Points of a Fractional Linear Transformation.- §6. Cauchy’s Theorem for Locally Integrable Vector Fields.- §7. More on Cauchy-Riemann.

Reviews

"The very understandable style of explanation, which is typical for this author, makes the book valuable for both students and teachers."
EMS Newsletter, Vol. 37, Sept. 2000 Fourth Edition S. Lang Complex Analysis "A highly recommendable book for a two semester course on complex analysis." —ZENTRALBLATTMATH