| 000 -LEADER |
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| fixed length control field |
nam a22 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
230831b xxu||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783031117985 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
515.43 |
| Item number |
TOR |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Torchinsky, Alberto |
| 245 ## - TITLE STATEMENT |
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| Title |
Modern view of the Riemann integral |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Name of publisher, distributor, etc |
Springer, |
| Date of publication, distribution, etc |
2022 |
| Place of publication, distribution, etc |
Cham : |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
x, 176 p. ; |
| Dimensions |
23 cm |
| Other physical details |
ill., |
| 365 ## - TRADE PRICE |
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| Price amount |
49.99 |
| Price type code |
EUR |
| Unit of pricing |
94.90 |
| 490 ## - SERIES STATEMENT |
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| Series statement |
Lecture notes in mathematics, |
| Volume number/sequential designation |
v.2309 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
This monograph uncovers the full capabilities of the Riemann integral. Setting aside all notions from Lebesgues theory, the author embarks on an exploration rooted in Riemanns original viewpoint. On this journey, we encounter new results, numerous historical vignettes, and discover a particular handiness for computations and applications. This approach rests on three basic observations. First, a Riemann integrability criterion in terms of oscillations, which is a quantitative formulation of the fact that Riemann integrable functions are continuous a.e. with respect to the Lebesgue measure. Second, the introduction of the concepts of admissible families of partitions and modified Riemann sums. Finally, the fact that most numerical quadrature rules make use of carefully chosen Riemann sums, which makes the Riemann integral, be it proper or improper, most appropriate for this endeavor. A Modern View of the Riemann Integral is intended for enthusiasts keen to explore the potential of Riemann's original notion of integral. The only formal prerequisite is a proof-based familiarity with the Riemann integral, though readers will also need to draw upon mathematical maturity and a scholarly outlook. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Riemann integral |
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| Topical term or geographic name as entry element |
Convergence Theorem |
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| Topical term or geographic name as entry element |
Coda |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
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| Item type |
Books |