TY  - BOOK
AU  - Terence Tao
TI  - Analysis I: : third edition
T2  - Texts and Readings in Mathematics
SN  - 9789380250649
AV  - QA300.TAO 
PY  - 2014///]
CY  - New Delhi
PB  - Hindustan Book Agency
KW  - Mathematics
N1  - 1. Introduction
2. Starting at the beginning: the natural numbers
3. Set theory
4. Integers and rationals
5. The real numbers
6. Limits of sequences
7. Series
8. Infinite sets
9. Continuous functions on R
10. Differentiation of functions
11. The Riemann integral
N2  - This is part one of a two-volume introduction to real analysis and is intended for honours undergraduates who have already been exposed to calculus. The emphasis is on rigour and on foundations. The material starts at the very beginning--the construction of the number systems and set theory--then goes on to the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and finally to 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. There are also appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of twenty-five to thirty lectures each. --- summary provided by publisher
ER  -