Ebook Advanced Real Analysis, by Anthony W. Knapp
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Advanced Real Analysis, by Anthony W. Knapp
Ebook Advanced Real Analysis, by Anthony W. Knapp
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* Presents a comprehensive treatment with a global view of the subject
* Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician
- Sales Rank: #2276987 in Books
- Brand: Brand: Birkhäuser
- Published on: 2005-07-27
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x 1.06" w x 6.14" l, 1.79 pounds
- Binding: Hardcover
- 466 pages
- Used Book in Good Condition
Review
From the reviews:
“It is useful both as a course text and for self-study. One can see, that its content is near all areas of pure mathematics, as well as applied mathematics, including statistics, mathematical physics, and differential equations. I think that and this volume turns to be useful for any mathematical library and can be recommended to students and lecturers.”(ZENTRALBLATT MATH)
From the Back Cover
Basic Real Analysis and Advanced Real Analysis (available separately or together as a Set) systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.
Key topics and features of Advanced Real Analysis:
* Develops Fourier analysis and functional analysis with an eye toward partial differential equations
* Includes chapters on Sturm–Liouville theory, compact self-adjoint operators, Euclidean Fourier analysis, topological vector spaces and distributions, compact and locally compact groups, and aspects of partial differential equations
* Contains chapters about analysis on manifolds and foundations of probability
* Proceeds from the particular to the general, often introducing examples well before a theory that incorporates them
* Includes many examples and nearly two hundred problems, and a separate 45-page section gives hints or complete solutions for most of the problems
* Incorporates, in the text and especially in the problems, material in which real analysis is used in algebra, in topology, in complex analysis, in probability, in differential geometry, and in applied mathematics of various kinds
Advanced Real Analysis requires of the reader a first course in measure theory, including an introduction to the Fourier transform and to Hilbert and Banach spaces. Some familiarity with complex analysis is helpful for certain chapters. The book is suitable as a text in graduate courses such as Fourier and functional analysis, modern analysis, and partial differential equations. Because it focuses on what every young mathematician needs to know about real analysis, the book is ideal both as a course text and for self-study, especially for graduate students preparing for qualifying examinations. Its scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, the clarity and breadth of Advanced Real Analysis make it a welcome addition to the personal library of every mathematician.
Most helpful customer reviews
21 of 24 people found the following review helpful.
Great book for real analysis
By Fadi
This is a fabulous book for learning real analysis. I've never taken a course in the subject (High school doesn't have one) but I have used the book for an independent study. After a fair study of point-set topology, this book can take you in and out of real analysis with ease. It's comprehensive and provides interesting insight into fields you thought you knew. It first tackles the problem of axiomatizing basic calculus, then it gives some background on metric spaces before hitting calculus of several variables and ordinary differential equations. The chapter on metric spaces was far more comprehensive than any I've read, and I've never seen a book that develops the theory of differential equations from an abstract perspective (none to this degree at least).
After this, it hits the meat of real analysis: Measure theory (and Lebesgue integration). Again, the author does an excellent job explaining and elaborating on this powerful theory. Euclidean spaces, topological spaces, L^p spaces, and Hilbert/Banach spaces take up the rest of this book. It even includes a very interesting chapter on Fourier transforms for Euclidean spaces. Overall, it's definitely worth the buy.
0 of 2 people found the following review helpful.
Clunky, needs editing....
By Nicholas Stevenson
This text is very thorough, and has many exercises with solutions and hints for solutions.
BUT.... it needs editing before I would use it as a course textbook for students learning this subject, as the presentation seems more tangled and turgid than necessary; I suspect that the author took the text material straight from his old notes. For example, on p. 578, Knapp gives the long, difficult proof of the Cantor-Schroeder-Bernstein theorem, instead of Koenig's short, beautiful, memorable proof from 1906). Or look at Corollary 1.5 on p.4. The last sentence of this proof is completely redundant as (n+1)/N from the previous sentence is a rational number between x and y.
Overall, a good text but Rudin is still better.
12 of 33 people found the following review helpful.
Kindle edition is unreadable
By Dave
The kindle edition has many unreadable equations in it.
I don't know the root cause (translation to kindle format, etc.)
The bottom line is some of the equations are worthless.
Don't buy this book in this format.
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