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Analysis II
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Catalogue Information
Field name
Details
Dewey Class
515
Title
Analysis II ([EBook]) / by Terence Tao.
Author
Tao, Terence , 1975-
Other name(s)
SpringerLink (Online service)
Edition statement
Third Edition
Publication
Singapore : Springer Singapore , 2016.
Physical Details
XVII, 220 pages : online resource.
Series
Texts and readings in mathematics
2366-8717 ; ; 38
ISBN
9789811018046
Summary Note
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. .:
Contents note
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.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-981-10-1804-6
Links to Related Works
Subject References:
Analysis
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Analysis (Mathematics)
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Mathematical analysis
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Mathematics
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Authors:
Tao, Terence 1975-
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Tao, Terence, 1975-
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Corporate Authors:
SpringerLink (Online service)
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Series:
Texts and readings in mathematics
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Classification:
515
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