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A guide to real variables / Steven G. Krantz.
- Format:
- Book
- Author/Creator:
- Krantz, Steven G. (Steven George), 1951- author.
- Series:
- Dolciani mathematical expositions ; no. 38.
- MAA guides ; no. 3.
- Dolciani mathematical expositions ; no. 38
- MAA guides ; no. 3
- Dolciani Mathematical Expositions, v. 38
- Language:
- English
- Subjects (All):
- Functions of real variables.
- Physical Description:
- 1 online resource (xvi, 147 pages) : digital, PDF file(s).
- Edition:
- 1st ed.
- Other Title:
- Real variables
- Place of Publication:
- Washington : Mathematical Association of America, 2009.
- Language Note:
- English
- Summary:
- A Guide to Real Variables provides aid and conceptual support for the student studying for the qualifying exam in real variables. Beginning with the foundations of the subject, the text moves rapidly but thoroughly through basic topics like completeness, convergence, sequences, series, compactness, topology and the like. All the basic examples like the Cantor set, the Weierstrass nowhere differentiable function, the Weierstrass approximation theory, the Baire category theorem, and the Ascoli-Arzela theorem are treated. The book contains over 100 examples, and most of the basic proofs. It illustrates both the theory and the practice of this sophisticated subject. Graduate students studying for the qualifying exams will find this book to be a concise, focused and informative resource. Professional mathematicians who need a quick review of the subject, or need a place to look up a key fact, will find this book to be a useful resource too. Steven Krantz is well-known for his skill in expository writing and this volume confirms it. He is the author of more than 50 books, and more than 150 scholarly papers. The MAA has awarded him both the Beckenbach Book Prize and the Chauvenet Prize.
- Contents:
- Basics
- Sequences
- Series
- The topology of the real line
- Limits and the continuity of functions
- The derivative
- The integral
- Sequences and series of functions
- Advanced topics.
- Notes:
- Title from publisher's bibliographic system (viewed on 02 Oct 2015).
- Includes bibliographical references (p. 141-142) and index.
- Description based on print version record.
- ISBN:
- 0-88385-916-5
- OCLC:
- 929120456
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