myArmoury.com: Undergraduate Analysis (Undergraduate Texts in Mathematics)

Undergraduate Analysis (Undergraduate Texts in Mathematics)

by Serge Lang

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Average customer rating:

(5 votes)

Edition: Hardcover

Other editions available: Hardcover, Digital, Hardcover

39 third-party copies available from: $23.00

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• Problems and Solutions for Undergraduate Analysis (Undergraduate Texts in Mathematics)
• Principles of Mathematical Analysis, Third Edition
• Counterexamples in Analysis (Dover Books on Mathematics)
• Real Mathematical Analysis
• Understanding Analysis

Product Description:

This is a logically self-contained introduction to analysis, suitable for students who have had two years of calculus. The book centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. Topics discussed include the classical test for convergence of series, Fourier series, polynomial approximation, the Poisson kernel, the construction of harmonic functions on the disc, ordinary differential equation, curve integrals, derivatives in vector spaces, multiple integrals, and others. In this second edition, the author has added a new chapter on locally integrable vector fields, has rewritten many sections and expanded others. There are new sections on heat kernels in the context of Dirac families and on the completion of normed vector spaces. A proof of the fundamental lemma of Lebesgue integration is included, in addition to many interesting exercises.

Accessories:
• Measure Theory
• Advanced Calculus: A Differential Forms Approach

Customer Reviews:

A beauty
Review date: 2005-07-12

I learned this material years ago but when I need to
look things up, this book has everything, well written.
For example the Taylor expansion with multinomial notation
is given here. The writer treats the undergraduate student's
intellect with respect. This is a serious book.

Just like every other Lang text
Review date: 2004-02-17

This book typifies Lang's style. If you enjoyed any of his other books you'll enjoy this too. Like seemingly all of his texts, it has a section on the inverse function theorem and makes quite a deal out of it. Overall, it is quite comprehensive, but there's little motivation for the proofs so things can be a bit boring. Both Rudin and Browder cover the same amout of material in far fewer pages, and they have better excerises too.

Solid, complete reference to basic analysis topics
Review date: 2003-04-14

Serge Lang's "Undergraduate Analysis" offers an impeccable selection of topics and exercises for the student wishing to broaden his/her knowledge of analysis. The proofs of theorems can be terse at times, but a hardworking student will gain much through a thorough reading of the text. Also, Lang concentrates many of his exercises on estimates, which is an art form that is slowly dying among undergraduates (and graduate students as well, sad to say). Many of his problems require only the triangle inequality (the basic tool of estimation) and ingenuity (and hard work) from the student. I would strongly recommend this text for anyone who wishes to fully understand and appreciate the results and techniques of basic real analysis.

okay
Review date: 2002-03-12

I personally don't care much for this book. It's too terse, and there are nowhere near enough examples. I have about 6 analysis books and this is the one I look in the least. It seems to cover a lot of stuff, but maybe too much-- it wouldve been better to focus more on some more elementary topics. For instance, he spends about one and a half pages introducing the derivative. So if you want a book that glosses over more elementary concepts and leans heavily toward a graduate level, this book's for you. At my school we were supposed to learn advanced calculus from this and it is not good for that at all. For advanced calc try robert stritchart's Way of Analysis (the best book on analysis I've ever read) and for analysis Intro to real analysis by kolmogrov (only 10 bucks or so and actually better than most books costing a 100)

Great intro to real analysis with logical format
Review date: 1999-07-22

Lang's book is an excellent introduction to real analysis that tries to build the reader's knowledge from the ground up. Lang starts with fundamental ideas from calculus and then proceeds in a logical way. Having taken Lang's course, for which this book was designed, it is clear to me that this book is a result of Lang's many years of experience teaching undergrads. I highly recommend this book to anyone who wants a solid foundation in analysis.

Product Details/Specifications:

Authors:
Serge Lang

Recording label: Springer
Publishers:
Springer

Manufacturer: Springer
EAN: 9780387948416
Binding: Hardcover
Dewey decimal number: 515.8
ISBN: 0387948414
Number of items: 1
Number of pages: 668
Publication date: 1996-12-05