Advanced real analysis along with a companion volume Basic real analysis
Literaturverz. S. 451 - 453
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Boston, Berlin u.a.
Birkhäuser
2005
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| Schriftenreihe: | Cornerstones
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| Schlagworte: | |
| Online Zugang: | Inhaltsverzeichnis Cover Inhaltstext Inhaltstext Publisher description |
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| Zusammenfassung: | Literaturverz. S. 451 - 453 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 problems It 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. TOC:Preface * Theory of calculus in one real variable * Metric spaces * Theory of differential calculus in several variables * Theory of ordinary differential equations and systems * Riemann integration in several variables * Abstract measure theory and Lebesgue measure * Measure theory for Euclidean space * Fourier transform in R^N * L^p spaces * Further topics in abstract measure theory * Topological spaces * Integration on locally compact spaces * Haar measure * Hilbert and Banach spaces * Distributions and their application to PDEs * References * Index |
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| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XXII, 465 S. 24 cm |
| ISBN: | 0817644075 0-8176-4407-5 0817643826 0-8176-4382-6 9780817643829 978-0-8176-4382-9 |