Hahn L., Epstein B. Classical Complex Analysis 1996

Textbook in PDF format

Classical Complex Analysis is a text that has been developed over decades of teaching with an enthusiastic student reception. The first half of the book focuses on the core material. An early chapter on power series gives the reader concrete examples of analytic functions and a review of calculus. Mobius transformations are presented with emphasis on the geometric aspect, and the Cauchy theorem is covered in the classical manner. The remaining chapters provide an elegant and solid overview of special topics such as Entire and Meromorphic Functions, Analytic Continuation, Normal Families, Conformal Mapping, and Harmonic Functions.
Complex Numbers
Power Series
Analytic Functions
The Cauchy Theorem
Singularities and Residues
The Maximum Modulus Principle
Entire and Meromorphic Functions
Analytic Continuation
Normal Families
Conformal Mapping
Harmonic Functions
The Picard Theorems
Appendix: Unsolved Problems
Index