文档介绍：A First Course in
Complex Analysis
Version
Matthias Beck, Gerald Marchesi, and Dennis Pixton
Department of Mathematics Department of Mathematical Sciences
San Francisco State University Binghamton University (SUNY)
San Francisco, CA 94132 Binghamton, NY 13902-6000
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Copyright 2002–2009 by the authors. All rights reserved. The most current version of this book is
available at the websites
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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.
2
These are the lecture notes of a one-semester undergraduate course which we have taught several
times at Binghamton University (SUNY) and San Francisco State University. 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.
We thank our students who made many suggestions for and found errors in the text. Special
thanks go to Collin Bleak, Jon Clauss, Sharma Pallekonda, and Joshua Palmatier ments
after teaching from this book.
Contents
plex Numbers 1
Definition and Algebraic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Geometric Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Elementary Topology of the Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Theorems from Calculus . . . . . . . . . . . . . . . . . . .