02270nam a2200337 u 4500001000800000005001700008008004100025020001800066035001200084040001300096041000800109082000800117100003500125245001600160250001100176260004300187300002000230490004300250500003200293520116900325650004001494650003101534650004001565650003001605650003401635650003801669650004101707942000901748999001901757952015601776132596720260508084350.0130502e20090312                    eng    a9788185931951  a1325967  ccomduadb  aeng 4a51510aTao, Terence4auteaut966949410aAnalysis II  a2. ed.  aIndia :bHindustan Book Agency,c2009.  axii, 350-566 p.0 aText and Readings in Mathematics ;v38  aGENERAL : Incluye índice.3 aThis 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 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. 7aAnálisis matemático2lemb91080  aEspacios métricos940037  aConvergencia (Matemáticas)929719  aSerie de potencias960901 7aSeries de Fourier2lemb95723 7aCálculo diferencial2lemb91670 7aIntegrales de Lebesgue2lemb9174726  cBOOK  c660296d660296  001040708GENaBCbBCd2013-05-02eAmazon.Comg75749.00iC1173588l3m2o515.2 T171 v2p0976223r2025-03-25 10:30:31s2025-02-21t1w2023-05-02yBOOK