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Varieties of integration /

Rosentrater, C. Ray.

Varieties of integration /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Varieties of integration // C. Ray Rosentrater.
作者:	Rosentrater, C. Ray.
出版者:	Washington, DC :Mathematical Association of America, : c2015.,
面頁冊數:	xv, 325 p. :ill. ; : 24 cm.;
標題:	Calculus, Integral. -
電子資源:	https://www.loc.gov/catdir/enhancements/fy1617/2015944846-b.html
電子資源:	https://www.loc.gov/catdir/enhancements/fy1617/2015944846-d.html
電子資源:	https://www.loc.gov/catdir/enhancements/fy1617/2015944846-t.html
ISBN:	9780883853597 :

Varieties of integration /
Rosentrater, C. Ray.

Varieties of integration /C. Ray Rosentrater. - Washington, DC :Mathematical Association of America,c2015. - xv, 325 p. :ill. ;24 cm. - Dolciani mathematical expositions ;no. 51. - Dolciani mathematical expositions ;no. 51..

Includes bibliographical references and index.

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.

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.--

ISBN: 9780883853597 :NT1795

LCCN: 2015944846Subjects--Topical Terms:

791995
Calculus, Integral.

LC Class. No.: QA308 / .R67 2015

Dewey Class. No.: 515.43

Varieties of integration /
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490 1 $a Dolciani mathematical expositions ; $v no. 51
504 $a Includes bibliographical references and index.
505 0 $a 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.
520 $a 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.-- $c Publisher.
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