Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka

• 216 pages and ten chapters for a one semester course
• Exercises at the end of each chapter with answers to selected exercises
• May be distributed and reproduced freely but not altered
• Paperback version from Orthogonal Publising for about $12
• In development and classroom use since 2002
• For more information and to download

This text grew out of the lecture notes of a single semester undergraduate course taught at Binghamton University (SUNY) and San Francisco State University, and it has benefited from the comments and suggestions from other instructors who have used the book. From the introduction:

For many of our students, Complex Analysis is their first rigorous analysis (if not mathematics) class they take, and this book reflects this very much. We tried to rely on as few concepts from real analysis as possible. In particular, series and sequences are treated from scratch, which has the (maybe disadvantageous) consequence that power series are introduced late in the course. The goal our book works toward is the Residue Theorem, including some nontraditional applications from both continuous and discrete mathematics.

The table of contents:

1. Complex Numbers
2. Differentiation
3. Examples of Functions
4. Integration
5. Consequences of Cauchy’s Theorem
6. Harmonic Functions
7. Power Series
8. Taylor and Laurent Series
9. Isolated Singularities and the Residue Theorem
10. Discrete Applications of the Residue Theorem