Analysis II : Third Edition / by Terence Tao

By:

Tao, Terence, 1975- [aut]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Texts and Readings in Mathematics ; 38 | SpringerLink BücherPublisher: Singapore : Springer, 2016Publisher: New Delhi : Hindustan Book Agency, 2016Description: Online-Ressource (XVII, 220 p, online resource)ISBN:

9789811018046
9789380250656

Subject(s):

Additional physical formats: 9789811018039 | 9789811018053 | Erscheint auch als: 9789811018039 Druck-Ausgabe | Erscheint auch als: 9789811018053 Druck-AusgabeMSC: MSC: *26-01 | 26Axx | 26Bxx | 28A12LOC classification:

QA299.6-433

DOI: DOI: 10.1007/978-981-10-1804-6Online resources:

Summary: Chapter 1. Metric Spaces -- Chapter 2. Continuous functions on metric spaces -- Chapter 3. Uniform convergence -- Chapter 4. Power series -- Chapter 5. Fourier series -- Chapter 6. Several variable differential calculus -- Chapter 7. Lebesgue measure -- Chapter 8. Lebesgue integration.Summary: This is part two of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory. .PPN: PPN: 1658613465Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA

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