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The following book has met the evaluation criteria developed by the AIM Editorial Board.

A First Course in Complex Analysis
  Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka

Digital versions pdf
Source available     Contact authors
Exercises Yes
Answers Yes
Solution Manual No
License Copyright held by authors

  • 127 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
  • Has been used and continues to be used at authors' institutions and elsewhere
  • 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 these notes reflect 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."
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