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Catalogue Information
Field name	Details
Dewey Class	515
Title	Analysis I ([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	XIX, 350 pages : online resource.
Series	Texts and readings in mathematics 2366-8717 ; ; 37
ISBN	9789811017896
Summary Note	This is part one 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. Introduction -- Chapter 2. Starting at the beginning: the natural numbers -- Chapter 3. Set theory -- Chapter 4. Integers and rationals -- Chapter 5. The real numbers -- Chapter 6. Limits of sequences -- Chapter 7. Series -- Chapter 8. Infinite sets -- Chapter 9. Continuous functions on R -- Chapter 10. Differentiation of functions -- Chapter 11. The Riemann integral. .
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/10.1007/978-981-10-1789-6
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Mathematical analysis . Mathematics . Authors: Tao, Terence 1975- . Corporate Authors: SpringerLink (Online service) . Series: Texts and readings in mathematics . Classification: 515 .

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Analysis I

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