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The third edition of this well known text continues to provide a
solid foundation in mathematical analysis for undergraduate and
first-year graduate students. The text begins with a discussion of
the real number system as a complete ordered field. (Dedekind's
construction is now treated in an appendix to Chapter I.) The
topological background needed for the development of convergence,
continuity, differentiation and integration is provided in Chapter
2. There is a new section on the gamma function, and many new and
interesting exercises are included. This text is part of the Walter
Rudin Student Series in Advanced Mathematics.
Function Theory in the Unit Ball of Cn. From the reviews:
..".The book is easy on the reader. The prerequisites are
minimal-just the standard graduate introduction to real analysis,
complex analysis (one variable), and functional analysis. This
presentation is unhurried and the author does most of the work.
...certainly a valuable reference book, and (even though there are
no exercises) could be used as a text in advanced courses." R.
Rochberg in Bulletin of the London Mathematical Society.
..".an excellent introduction to one of the most active research
fields of complex analysis. ...As the author emphasizes, the
principal ideas can be presented clearly and explicitly in the
ball, specific theorems can be quickly proved. ...Mathematics lives
in the book: main ideas of theorems and proofs, essential features
of the subjects, lines of further developments, problems and
conjectures are continually underlined. ...Numerous examples throw
light on the results as well as on the difficulties."
C. Andreian Cazacu in Zentralblatt fur Mathematik"
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