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Record Nr. |
UNISA996495170503316 |
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Autore |
Torchinsky Alberto |
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Titolo |
A modern view of the Riemann integral / / Alberto Torchinsky |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2022] |
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©2022 |
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ISBN |
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9783031117992 |
9783031117985 |
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Descrizione fisica |
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1 online resource (182 pages) |
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Collana |
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Lecture Notes in Mathematics ; ; v.2309 |
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Disciplina |
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Soggetti |
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Riemann integral |
Integral de Riemann |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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. |
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