Matthias Beck, Gerald Marchesi, Dennis Pixton, and Lucas Sabalka
A First Course in Complex Analysis was written for a one-semester undergraduate course developed at Binghamton University (SUNY) and San Francisco State University, and has been adopted at several other institutions. For many of our students, Complex Analysis is their first rigorous analysis (if not mathematics) class they take, and this book 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, 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.
Instructors can request a partial solutions manual by email.
Our book is featured in the Open Textbook Initiative by the American Institute of Mathematics. 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