02168nam a2200349uu 4500001000800000005001700008008004100025020001800066035001200084040001300096041000800109082000800117100002700125245001500152250001100167260004300178300001600221490004300237500004600280520116900326650003401495650002401529650002201553650002501575650002701600650002701627650003301654650001601687650003801703650003101741650004601772131940320260508075555.0130312e20090312                    eng    a9788185931944  a1319403  ccomduadb  aeng 4a51510aTao, Terence4auteaut10aAnalysis I  a2. ed.  aIndia :bHindustan Book Agency,c2009.  axvi, 350 p.0 aText and Readings in Mathematics ;v37  aGENERAL : Incluye apéndices e índice.3 aThis 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. 7aAnálisis matemático2lemb  aNúmeros naturales  aNúmeros enteros  aNúmeros racionales 7aNúmeros reales2lemb 7aSeries infinitas2lemb 7aSeries (Matemáticas)2lemb  aContinuidad  aIntegrales de Riemann - Stieltjes  aSecuencias (matemáticas) 7aLógica simbólica y matemática2lemb