A First Course in Complex Analysis

Matthias Beck, Gerald Marchesi, Dennis Pixton, and Lucas Sabalka

These are the lecture notes of a one-semester undergraduate course which we used at SUNY Binghamton and San Francisco State (and which have been adopted at many other institutions). 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." This also has the (maybe disadvantageous) consequence that power series are introduced very late in the course.

The lecture notes are available in pdf format. To view them you may download Acrobat Reader.

Copyright 2002-2014 by the authors. All rights reserved. This book may be freely reproduced and distributed, provided that it is reproduced in its entirety from the most recent version. This book may not be altered in any way, except for changes in format required for printing or other distribution, without the permission of the authors.

We would be happy to hear from anyone who has adopted our book for their course, as well as suggestions, corrections, or other comments.


"First, it is neccessary to study the facts, to multiply the number of observations, and then later to search for formulas that connect them so as thus to discern the particular laws governing a certain class of phenomena. In general, it is not until after these particular laws have been established that one can expect to discover and articulate the more general laws that complete theories by bringing a multitude of apparently very diverse phenomena together under a single governing principle."
Augustin Louis Cauchy