TY  - GEN
AU  - Tao,Terence
TI  - Analysis II
T2  - Texts and Readings in Mathematics
SN  - 9788195196128
U1  - 515 23rd
PY  - 2022///
CY  - New Delhi
PB  - HBA
KW  - Mathematics
KW  - Analysis
KW  - Lebesgue integration
KW  - Fourier Series
N1  - Includes index; Metric spaces -- Continuous functions on metric spaces -- Uniform convergence -- Power series -- Fourier series -- Several variable differential calculus -- Lebesgue measure -- Lebesgue integration
N2  - This is part two 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.

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.

The fourth edition incorporates a large number of additional corrections reported since the release of the third edition, as well as some additional exercises
ER  -