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Can I read A Modern View of the Riemann Integral on EtoBox?
A Modern View of the Riemann Integral by Alberto Torchinsky is a nonfiction available to read on EtoBox.
What is A Modern View of the Riemann Integral about?
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 scholarl
Who reads A Modern View of the Riemann Integral?
It is typically read by self-directed learners exploring a subject in depth.
Common subject areas: history, science, philosophy, social sciences.
- Author
- Alberto Torchinsky
- Publisher
- Springer International Publishing : Imprint: Springer
- Published
- 2022
- Language
- EN
- ISBN
- 9783031117985
- Category
- nonfiction
- Subjects
- Mathematics, Stem