01995nam a2200301 u 4500001000800000005001700008008004100025020001800066035001200084040001300096041000800109082000800117100002700125245001600152250001100168260004300179300002000222490004300242500003200285520116900317650003401486650002401520650003301544650002301577650002801600650003201628650003301660132596720260508084350.0130502e20090312                    eng    a9788185931951  a1325967  ccomduadb  aeng 4a51510aTao, Terence4auteaut10aAnalysis 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 matemático2lemb  aEspacios métricos  aConvergencia (Matemáticas)  aSerie de potencias 7aSeries de Fourier2lemb 7aCálculo diferencial2lemb 7aIntegrales de Lebesgue2lemb