# Analysis II: 3rd Edition

## Book Description

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.

### Table of Contents

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

## Book Details

- Title: Analysis II: 3rd Edition
- Author: Terence Tao
- Length: 220 pages
- Edition: 1st ed. 2016
- Language: English
- Publisher: Springer
- Publication Date: 2016-09-21
- ISBN-10: 9811018030
- ISBN-13: 9789811018039

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