02528nam 2200469 450 991061620990332120231110231300.09783031117992(electronic bk.)9783031117985(MiAaPQ)EBC7107451(Au-PeEL)EBL7107451(CKB)24996020900041(PPN)265855322(EXLCZ)992499602090004120230303d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierA modern view of the Riemann integral /Alberto TorchinskyCham, Switzerland :Springer,[2022]©20221 online resource (182 pages)Lecture Notes in Mathematics ;v.2309Print version: Torchinsky, Alberto A Modern View of the Riemann Integral Cham : Springer International Publishing AG,c2022 9783031117985 Includes bibliographical references and index.Intro -- 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.Lecture Notes in Mathematics Riemann integralIntegral de RiemannthubLlibres electrònicsthubRiemann integral.Integral de Riemann618Torchinsky Alberto42422MiAaPQMiAaPQMiAaPQ9910616209903321Modern View of the Riemann Integral3390105UNINA