Advanced Real Analysis (Hardcover)
Language: English
Published by Birkhauser Boston Inc, Secaucus, 2005
Series: Book 4 of 12 - Cornerstones
- Hardcover
- New
Seller: Grand Eagle Retail, Bensenville, IL, U.S.A.Grand Eagle Retail
AbeBooks seller since October 12, 2005
Condition: New
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Hardcover. Advanced Real Analysis systematically develops the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established. This work presents 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: - Early chapters treat the fundamentals of real variables, the theory of Fourier series for the Riemann integral, and the theoretical underpinnings of multivariable calculus and differential equations - Subsequent chapters develop measure theory, point-set topology, Fourier series for the Lebesgue integral, and the basics of Banach and Hilbert spaces - Later chapters provide a higher-level view of the interaction between real analysis and algebra, including functional analysis, partial differential equations, and further topics in Fourier analysis - Throughout the text are problems that develop and illuminate aspects of the theory of probability - Includes many examples and hundreds of problems, and a chapter gives hints or complete solutions for most of the problemsIt requires of the reader only familiarity with some linear algebra and real variable theory, a few weeks' worth of group theory, and an acquaintance with proofs. Because it focuses on what every young mathematician needs to know about real analysis, this book is ideal both as a course text and for self-study, especially for graduate students preparing for qualifying examinations.Its scope and unique 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, math physics, and applied differential equations. Indeed, the clarity and breadth of Advanced Real Analysis make it a welcome addition to the personal library of every mathematician. Advanced Real Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.…
Seller Inventory # 9780817643829
- Title
- Advanced Real Analysis (Hardcover)
- Author
- Anthony W. Knapp
- Publisher
- Birkhauser Boston Inc, Secaucus
- Publication year
- 2005
- Condition
- new
- Binding
- Hardcover
- Language
- English
- ISBN 10
- 0817643826
- ISBN 13
- 9780817643829
- Series
- Book 4 of 12: Cornerstones
* 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
"Synopsis" may belong to another edition of this title.
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.
"About the title" may belong to another edition of this title.
Grand Eagle Retail
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