LEADER 02702nam 2200517 450 001 996511862803316 005 20231009150058.0 010 $a981-19-7284-2 010 $z9788195196128 024 7 $a10.1007/978-981-19-7284-3 035 $a(MiAaPQ)EBC7205353 035 $a(Au-PeEL)EBL7205353 035 $a(CKB)26170315000041 035 $a(DE-He213)978-981-19-7284-3 035 $a(PPN)268207291 035 $a(EXLCZ)9926170315000041 100 $a20230519d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAnalysis II /$fTerence Tao 205 $aFourth edition. 210 1$aGateway East, Singapore :$cSpringer,$d[2023] 210 4$d©2023 215 $a1 online resource (208 pages) 225 1 $aTexts and Readings in Mathematics,$x2366-8725 ;$v38 311 08$aPrint version: Tao, Terence Analysis II Singapore : Springer,c2023 327 $aChapter 1. Metric Spaces -- Chapter 2. Continuous functions on metric spaces -- Chapter 3. Uniform convergence -- Chapter 4. Power series -- Chapter 5. Fourier series -- Chapter 6. Several variable differential calculus -- Chapter 7. Lebesgue measure -- Chapter 8. Lebesgue integration. 330 $aThis is the second book of a two-volume textbook on real analysis. Both the volumes?Analysis I and Analysis II?are intended for honors undergraduates who have already been exposed to calculus. The emphasis is on rigor and foundations. The material starts at the very beginning?the construction of number systems and set theory (Analysis I, Chaps. 1?5), then on to the basics of analysis such as limits, series, continuity, differentiation, and Riemann integration (Analysis I, Chaps. 6?11 on Euclidean spaces, and Analysis II, Chaps. 1?3 on metric spaces), through power series, several variable calculus, and Fourier analysis (Analysis II, Chaps. 4?6), and finally to the Lebesgue integral (Analysis II, Chaps. 7?8). There are appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) is taught in two quarters of twenty-five to thirty lectures each. 410 0$aTexts and Readings in Mathematics,$x2366-8725 ;$v38 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 $a996511862803316 996 $aAnalysis II$91523143 997 $aUNISA