TY  - BOOK
AU  - Tao,Terence
TI  - Analysis I
T2  - Text and Readings in Mathematics
SN  - 9788185931944
U1  - 515 
PY  - 2009///
CY  - India
PB  - Hindustan Book Agency
KW  - Análisis matemático
KW  - lemb
KW  - Números naturales
KW  - Números enteros
KW  - Números racionales
KW  - Números reales
KW  - Series infinitas
KW  - Series (Matemáticas)
KW  - Continuidad
KW  - Integrales de Riemann - Stieltjes
KW  - Secuencias (matemáticas)
KW  - Lógica simbólica y matemática
N1  - GENERAL : Incluye apéndices e índice
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 fundations. The material starts at the very beginning-the constrruction of 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 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.
In this second edition, several typos and other errors have been corrected
ER  -