1.

Record Nr.

UNINA9910616209903321

Autore

Torchinsky Alberto

Titolo

A modern view of the Riemann integral / / Alberto Torchinsky

Pubbl/distr/stampa

Cham, Switzerland : , : Springer, , [2022]

©2022

ISBN

9783031117992

9783031117985

Descrizione fisica

1 online resource (182 pages)

Collana

Lecture Notes in Mathematics ; ; v.2309

Disciplina

618

Soggetti

Riemann integral

Integral de Riemann

Llibres electrònics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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.