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Analysis II

Third Edition

  • Textbook
  • © 2016

Overview

Authors:
  1. Terence Tao

    1. Department of Mathematics, Univ of California, Los Angeles Department of Mathematics, Los Angeles, USA

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  • 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)

  1. Front Matter

    Pages i-xvii
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  2. Metric spaces

    • Terence Tao
    Pages 1-27

  3. Continuous functions on metric spaces

    • Terence Tao
    Pages 28-44

  4. Uniform convergence

    • Terence Tao
    Pages 45-74

  5. Power series

    • Terence Tao
    Pages 75-106

  6. Fourier series

    • Terence Tao
    Pages 107-126

  7. Several Variable Differential Calculus

    • Terence Tao
    Pages 127-161

  8. Lebesgue measure

    • Terence Tao
    Pages 162-186

  9. Lebesgue integration

    • Terence Tao
    Pages 187-211

  10. Back Matter

    Pages 213-220
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Keywords

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

  • Department of Mathematics, Univ of California, Los Angeles Department of Mathematics, Los Angeles, USA

    Terence Tao

About the author

Terence "Terry" Chi-Shen Tao, FAA FRS, is an Australian mathematician. His areas of interests are in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing and analytic number theory. As of 2015, he holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles. Professor Tao is a co-recipient of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics. He maintains a personal mathematics blog, which has been described by Timothy Gowers as “the undisputed king of all mathematics blogs”.

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

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