Authors:
- Discusses all major topics of analysis in a simple, lucid manner
- Highlights the concrete setting of the real line and Euclidean spaces
- Provides examples, and step-by-step instructions
- Evolves from the author’s lectures delivered at the University of California, Los Angeles
- Covers about 30 lectures, this is part two of the two-volume book
- Is authored by the winner of the Fields Medal
- Includes supplementary material: sn.pub/extras
Part of the book series: Texts and Readings in Mathematics (TRIM, volume 38)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
About this book
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.
Authors and Affiliations
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Department of Mathematics, Univ of California, Los Angeles Department of Mathematics, Los Angeles, USA
Terence Tao
About the author
Bibliographic Information
Book Title: Analysis II
Book Subtitle: Third Edition
Authors: Terence Tao
Series Title: Texts and Readings in Mathematics
DOI: https://doi.org/10.1007/978-981-10-1804-6
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2016
eBook ISBN: 978-981-10-1804-6Published: 22 August 2016
Series ISSN: 2366-8717
Series E-ISSN: 2366-8725
Edition Number: 1
Number of Pages: XVII, 220
Topics: Analysis