Mathematical Analysis: An Introduction (Undergraduate Texts in Mathematics) | 
 enlarge | Author: Andrew Browder
Publisher: Springer
Category: Book
List Price: $59.95
Buy New: $39.49
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Rating:  9 reviews
Sales Rank: 234193
Media: Hardcover
Edition: Corrected
Pages: 333
Number Of Items: 1
Shipping Weight (lbs): 1.4
Dimensions (in): 9.3 x 6.7 x 1
ISBN: 0387946144
Dewey Decimal Number: 515
EAN: 9780387946146
Publication Date: January 25, 2001
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Product Description
This is a textbook suitable for a year-long course in analysis at the advanced undergraduate or beginning graduate level. It is intended for students with a strong background in calculus and linear algebra. The first semester of this course is the basic introductory course in analysis, introducing the words "compact", "complete" " connected", "continuous", "convergent", etc. Among traditional purposes of such a course is the training of a student in the conventions of pure mathematics: acquiring a feeling for what is considered a proof, and supplying literate written arguments to support mathematical propositions. The topics covered in the second semester, and the second half of this book, are differentiation (of vector-valued functions of several variables), integration, and the connection between these concepts which is displayed in the theorem of Stokes, in its general form. Also included are some beautiful applications of the theory such as Brouwer's fixed point theorem, and the Dirichlet principle for harmonic functions.
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| Customer Reviews: Read 4 more reviews...
 Concise and extremely well written book February 11, 1999
8 out of 9 found this review helpful
This is a very well written book. It is concise, rigorous and contains all the usual material of an undergraduate analysis course. I prefer the treatment of manifolds and differential forms in this book to that given in Rudins' classic book.
A wonderful first book in analysis August 15, 2001
Juan David Gonzalez Cobas (Gijon, Asturias Spain)
8 out of 11 found this review helpful
Browder's book is a great text for serious study of analysis at the beginning level. The coverage is similar to Rudin's "Principles of MA", and it is a worthy successor of it. It is a book for mathematicians, so don't even dare to open it if you are looking for the usual 'calculus for dummies' course. Proofs are usually the most concise and elegant ones, being in the tradition of Rudin again. But the treatment of analysis on manifolds is more standard, just as the construction of Lebesgue measure and integration. Only drawbacks: sticking to real variable and omitting complex numbers on most subjects (even in power series!), and the ominous presence of the usual chapter on Riemann integral. You may buy Rudin or this, and you'll be doing a great investment.
Best Selection of Topics September 2, 2005
Matthew N. Moore (Chapel Hill, NC)
1 out of 1 found this review helpful
I've read a few books on Real Analysis. Some attempt to cover too much, some don't cover enough. This book seems to include all of the essential topics without going overboard. It is also very easy to navigate.
Concise, rigorous text August 20, 2006
Sreeram Dhurjaty (Rochester, NY)
1 out of 1 found this review helpful
This book is for serious students of mathematics. A certain amount of mathematical maturity is needed in order to, fully, appreciate this book. It is also necessary to work through the examples in order to derive the greatest value from this text. Having studied, mathematics, over various years, from texts by Hardy, Rudin, Royden etc., I feel that this book is a worthwhile addition to the armamentarium of a serious student who is interested in learning the tools of rigorous analysis.
If I could, I would hypnotize you and make you buy this book August 7, 2002
10 out of 23 found this review helpful
This is the best book for Stoke's Theorem. The machinery of the Lebesgue integral is used to simplify the integration on manifolds theory. This is very nice and very not ad hoc.voo de voo de vooooo....I am hypnotizing you......voo de voo......You must buy this book....vooooo.....book good....voo de voo de voo....better than Calculus on Manifolds....voo de voooo....
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