PROBLEMS AND SOLUTIONS FOR COMPLEX ANALYSIS

This volume contains all the exercises, and their solutions, for Serge Lang's fourth edition of "Complex Analysis," ISBN 0-387-98592-1. The problems in the first 8 chapters are suitable for an introductory course at the undergraduate level and cover the following topics: power series, Cauchy's theorem, Laurent series, singularities and meromorphic functions, the calculus of residues, conformal mappings, and harmonic functions. The material in Chapters 9-16 is more advanced. The reader will find problems on Schwartz reflection, analytic continuation, Jensen's formula, the Phragmen-Lindeloef theorem, entire functions, Weierstrass products and meromorphic functions, the Gamma function and Zeta function. This volume also serves as an independent source of problems with detailed answers beneficial for anyone interested in learning complex analysis. TOC:Complex Numbers and Functions.- Power Series.- Cauchy's Theorem, First Part.- Winding Numbers and Cauchy's Theorem.- Applications of Cauchy's Integral Formula.- Calculus of Residues.- Conformal Mappings.- Harmonic Functions.- Schwarz Reflection.- The Riemann Mapping Theorem.- Analytic Continuation Along Curves.- Applications of the Maximum Modulus Principle and Jensen's Formula.- Entire and Meromorphic Functions.- Elliptic Functions.- The Gamma and Zeta Functions.- The Prime Number Theorem.- Appendix.