LEADER 02757nam 2200517 450 001 996511862703316 005 20231009161940.0 010 $a981-19-7261-3 010 $a9789811972614 010 $z9788195196197 024 7 $a10.1007/978-981-19-7261-4 035 $a(MiAaPQ)EBC7205363 035 $a(Au-PeEL)EBL7205363 035 $a(CKB)26170317600041 035 $a(DE-He213)978-981-19-7261-4 035 $a(PPN)268207283 035 $a(EXLCZ)9926170317600041 100 $a20230604d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAnalysis I /$fTerence Tao 205 $aFourth edition. 210 1$aSingapore :$cSpringer,$d2022. 215 $a1 online resource (301 pages) 225 1 $aTexts and readings in mathematics ;$v37 311 08$aPrint version: Tao, Terence Analysis I Singapore : Springer,c2023 327 $aChapter 1. Introduction -- Chapter 2. Starting at the beginning: the natural numbers -- Chapter 3. Set theory -- Chapter 4. Integers and rationals -- Chapter 5. The real numbers -- Chapter 6. Limits of sequences -- Chapter 7. Series -- Chapter 8. Infinite sets -- Chapter 9. Continuous functions on R -- Chapter 10. Differentiation of functions -- Chapter 11. The Riemann integral. . 330 $aThis is the first book of a two-volume textbook on real analysis. Both the volumes?Analysis I and Analysis II?are intended for honors undergraduates who have already been exposed to calculus. The emphasis is on rigor and foundations. The material starts at the very beginning?the construction of number systems and set theory (Analysis I, Chaps. 1?5), then on to the basics of analysis such as limits, series, continuity, differentiation, and Riemann integration (Analysis I, Chaps. 6?11 on Euclidean spaces, and Analysis II, Chaps. 1?3 on metric spaces), through power series, several variable calculus, and Fourier analysis (Analysis II, Chaps. 4?6), and finally to the Lebesgue integral (Analysis II, Chaps. 7?8). There are appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) is in two quarters of twenty-five to thirty lectures each. 410 0$aTexts and readings in mathematics ;$v37. 606 $aMathematical analysis 606 $aAnàlisi matemàtica$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematical analysis. 615 7$aAnàlisi matemàtica 676 $a515 700 $aTao$b Terence$0477043 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996511862703316 996 $aAnalysis I$91523142 997 $aUNISA