LEADER 02528nam 2200469 450 001 9910616209903321 005 20231110231300.0 010 $a9783031117992$b(electronic bk.) 010 $z9783031117985 035 $a(MiAaPQ)EBC7107451 035 $a(Au-PeEL)EBL7107451 035 $a(CKB)24996020900041 035 $a(PPN)265855322 035 $a(EXLCZ)9924996020900041 100 $a20230303d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA modern view of the Riemann integral /$fAlberto Torchinsky 210 1$aCham, Switzerland :$cSpringer,$d[2022] 210 4$d©2022 215 $a1 online resource (182 pages) 225 1 $aLecture Notes in Mathematics ;$vv.2309 311 08$aPrint version: Torchinsky, Alberto A Modern View of the Riemann Integral Cham : Springer International Publishing AG,c2022 9783031117985 320 $aIncludes bibliographical references and index. 327 $aIntro -- Preface -- Contents -- 1 Introduction -- 2 The -Riemann Integral -- 2.1 The Volume of a Lake -- 2.2 Rate of Approximation -- 2.3 Quadrature Rules -- 2.4 Roots of Nonlinear Equations -- Monotonicity of Riemann Sums -- 3 A Convergence Theorem -- 3.1 The Riemann-Lebesgue Lemma -- 3.2 The Weierstrass Approximation Theorems -- 4 The Modified -Riemann Sums -- 4.1 Uniformly Distributed Sequences -- 5 The Pattern and Uniform Integrals -- 6 The Improper and Dominated Integrals -- 6.1 Improper Integrals of the First Type -- 6.2 The Dominated Integral -- 6.3 Improper Integrals of the Second Type -- 7 Coda -- Appendix I -- Appendix I -- Change of Variable Formulas for Riemann Integrals -- The Substitution Formula -- The Substitution Formula -- Change of Variable Formula, Riemann Integral -- Substitution Formula, Riemann-Stieltjes Integral -- Change of Variable Formula, Riemann-Stieltjes Integral -- Caveat -- Appendix II -- Appendix II -- Cauchy Integrability Implies Riemann Integrability -- References -- Index. 410 0$aLecture Notes in Mathematics 606 $aRiemann integral 606 $aIntegral de Riemann$2thub 608 $aLlibres electrònics$2thub 615 0$aRiemann integral. 615 7$aIntegral de Riemann 676 $a618 700 $aTorchinsky$b Alberto$042422 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910616209903321 996 $aModern View of the Riemann Integral$93390105 997 $aUNINA