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  3. Reel analyse, reelle variabler

A Modern View of the Riemann Integral

Af: Alberto Torchinsky Engelsk Paperback

A Modern View of the Riemann Integral

Af: Alberto Torchinsky Engelsk Paperback
Tjek vores konkurrenters priser

This monograph uncovers the full capabilities of the Riemann integral. Setting aside all notions from Lebesgue''s theory, the author embarks on an exploration rooted in Riemann''s 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.

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This monograph uncovers the full capabilities of the Riemann integral. Setting aside all notions from Lebesgue''s theory, the author embarks on an exploration rooted in Riemann''s 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.

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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 176
ISBN-13: 9783031117985
Indbinding: Paperback
Udgave:
ISBN-10: 3031117980
Kategori: Reel analyse, reelle variabler
Udg. Dato: 6 okt 2022
Længde: 0mm
Bredde: 155mm
Højde: 235mm
Forlag: Springer International Publishing AG
Oplagsdato: 6 okt 2022
Forfatter(e): Alberto Torchinsky
Forfatter(e) Alberto Torchinsky

Kategori Reel analyse, reelle variabler

ISBN-13 9783031117985

Sprog Engelsk

Indbinding Paperback

Sider 176

Udgave

Længde 0mm

Bredde 155mm

Højde 235mm

Udg. Dato 6 okt 2022

Oplagsdato 6 okt 2022

Forlag Springer International Publishing AG

Kategori sammenhænge