國立虎尾科技大學 |

Language: English

Back

Varieties of integration /

Rosentrater, C. Ray.

Varieties of integration /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Varieties of integration // C. Ray Rosentrater.
Author:	Rosentrater, C. Ray.
Published:	Washington, DC :Mathematical Association of America, : c2015.,
Description:	xv, 325 p. :ill. ; : 24 cm.;
Subject:	Calculus, Integral. -
Online resource:	https://www.loc.gov/catdir/enhancements/fy1617/2015944846-b.html
Online resource:	https://www.loc.gov/catdir/enhancements/fy1617/2015944846-d.html
Online resource:	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 /
LDR:02514cam a2200313 a 4500 001 903170
005 20190211103055.0
008 190226s2015 dcua b 001 0 eng d
010 $a 2015944846
020 $a 9780883853597 : $c NT1795
020 $a 0883853590
020 $a 9781614442172 (ebk.)
020 $a 1614442177 (ebk.)
035 $a (OCoLC)ocn932003103
035 $a 18671970
040 $a YDXCP $b eng $c YDXCP $d EYD $d OCLCF $d VLR $d DLC $d NFU
041 0 $a eng
042 $a lccopycat
050 0 0 $a QA308 $b .R67 2015
082 0 4 $a 515.43 $2 23
100 1 $a Rosentrater, C. Ray. $3 1171167
245 1 0 $a Varieties of integration / $c C. Ray Rosentrater.
260 $a Washington, DC : $b Mathematical Association of America, $c c2015.
300 $a xv, 325 p. : $b ill. ; $c 24 cm.
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.
650 0 $a Calculus, Integral. $3 791995
650 0 $a Integrals. $3 528410
830 0 $a Dolciani mathematical expositions ; $v no. 51. $3 1171168
856 4 2 $3 Contributor biographical information $u https://www.loc.gov/catdir/enhancements/fy1617/2015944846-b.html
856 4 2 $3 Publisher description $u https://www.loc.gov/catdir/enhancements/fy1617/2015944846-d.html
856 4 1 $3 Table of contents only $u https://www.loc.gov/catdir/enhancements/fy1617/2015944846-t.html