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Varieties of integration

Author: C Ray Rosentrater
Publisher: [Washington, DC] : Mathematical Association of America, [2015] ©2015
Series: Dolciani mathematical expositions, no. 51.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Varieties of Integration explores the critical contributions by Riemann, Darboux, Lebesgue, Henstock, Kurzweil, and Stieltjes to the theory of integration and provides a glimpse of more recent variations of the integral such as those involving operator-valued measures. By the first year of graduate school, a young mathematician will have encountered at least three separate definitions of the integral. The associated  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Rosentrater, C. Ray.
Varieties of integration.
Washington, DC : Mathematical Association of America, [2015]
(DLC) 2015944846
(OCoLC)932003103
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: C Ray Rosentrater
ISBN: 9781614442172 1614442177
OCLC Number: 947859142
Description: 1 online resource (xv, 325 pages) : illustrations.
Contents: Historical introduction --
The Riemann integral --
The Darboux integral --
A functional zoo --
Another approach : measure theory --
The Lebesgue integral --
The Gauge integral --
Stieltjes-type integrals and extensions --
A look back --
Afterword : L₂ spaces and Fourier series.
Series Title: Dolciani mathematical expositions, no. 51.
Responsibility: C. Ray Rosentrater, Westmont College.

Abstract:

Varieties of Integration explores the critical contributions by Riemann, Darboux, Lebesgue, Henstock, Kurzweil, and Stieltjes to the theory of integration and provides a glimpse of more recent variations of the integral such as those involving operator-valued measures. By the first year of graduate school, a young mathematician will have encountered at least three separate definitions of the integral. The associated integrals are typically studied in isolation with little attention paid to the relationships between them or to the historical issues that motivated their definitions. Varieties of Integration redresses this situation by introducing the Riemann, Darboux, Lebesgue, and gauge integrals in a single volume using a common set of examples. This approach allows the reader to see how the definitions influence proof techniques and computational strategies. Then the properties of the integrals are compared in three major areas: the class of integrable functions, the convergence properties of the integral, and the best form of the fundamental theorems of calculus.--Publisher.

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