# Complex Analysis, by T. W. Gamelin

### Publication Information

First printing: 2001

Publisher: Springer-Verlag, New York, Inc.

Textbook series: Undergraduate Texts in Mathematics

ISBN 0-387-95093-1 (hardcover)

ISBN 0-387-95069-9 (softcover)

The
Springer web site
for the book has more information, including links to pdf files for
Chapters IV and IX of the book.
### Solutions to Exercises

Anders Nordborg is building a web site with solutions to many of
the
exercises, at:

www.sb.hik.se/personal/sanno/index.htm

### List of Errata in Second Printing

List of errata, compiled June 19, 2006: (.pdf)
### Changes to First Printing

List of changes made from first to second printing:
(.pdf)
#### Comments on Changes

There were two "major" gaffes in the first printing, which were
corrected for the second printing as follows:
- Page 282: Exercises 3-5 in Section X.2 were replaced by substitute
Exercises 3 and 4 in the list of changes. Also, Exercise 2 on page 282
was expanded, so that the combined changes fit exactly the same number
of lines as in the original version.

- Page 406: The "potential theory" proof of the Riemann mapping
theorem is incomplete. The function used in the proof is not a barrier,
according to the definition given in the book. Something nontrivial
must be done (Bouligand's lemma) to construct a barrier. The
replacement in the second printing refers to Tsuji's book for the
Bouligand lemma. Another good source is the book "Complex Potential
Theory" by T.J. Ransford. I'll post soon a complete proof on this web
site.

There are various kinds of changes made for the second printing:
- Some of the changes are rather trivial (font, spelling, minor
grammatical infringements, and so on).

- Some of the changes correct errors that were undoubtedly
evident to the reader, such as mislabeled contours, mistaken exercise
reference labels, and simple typographical mistakes.

- Some of the changes correct errors that were more substantial,
though still probably evident to the instructor. For instance, the
statement in Exercise XVI.1.3(b) on p.423 is flagrantly false, and a
correct substitute exercise has been provided in the list of changes.

- Some of the exercises are "undoable," a fact which became apparent
to me in the course of preparing a solution manual. For instance,
Exercises XV.4-5 on pp.405-406 are correct but undoable on the basis of
the treatment in the book. Substitute exercises are provided in the
list of changes.

- Some of the changes are made to increase or decrease the number of
lines, so that no repagination is required.

My thanks go to the people (with special thanks to Bob Burckel) who
have pointed out to me various errata in the first printing. I'm very
happy to receive further comments on errata and expository lapses. My
email address is

twg@math.ucla.edu.

I thank you in advance. -- Ted Gamelin