Matthias Beck, Gerald Marchesi, Dennis Pixton, and Lucas Sabalka
These are the lecture notes of a one-semester undergraduate course which we taught at SUNY Binghamton and San Francisco State. 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.
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"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