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Dolciani Mathematical Expositions Ser.: Varieties of Integration by C. Ray Rosentrater (2015, Hardcover)
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Varieties of Integration, Hardcover by Rosentrater, C. Ray, ISBN 0883853590, ISBN-13 9780883853597, Brand New, Free shipping in the US A textbook that studies and compares the various different types of integration that young mathematicians encounter.
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About this product
Product Identifiers
PublisherAmerican Mathematical Society
ISBN-100883853590
ISBN-139780883853597
eBay Product ID (ePID)220461325
Product Key Features
Number of Pages326 Pages
Publication NameVarieties of Integration
LanguageEnglish
Publication Year2015
SubjectCalculus, Mathematical Analysis
TypeTextbook
Subject AreaMathematics
AuthorC. Ray Rosentrater
SeriesDolciani Mathematical Expositions Ser.
FormatHardcover
Dimensions
Item Height0.8 in
Item Weight19.9 Oz
Item Length9 in
Item Width6 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2015-944846
ReviewsThis is a handsomely produced book (like most MAA publications), and it appears to be of just the right length and at the right level for the intended audience." - CMS Notices, This is a handsomely produced book (like most MAA publications), and it appears to be of just the right length and at the right level for the intended audience."" - CMS Notices
Dewey Edition23
Series Volume Number51
IllustratedYes
Dewey Decimal515.43
Table Of ContentPreface 1. Historical Introduction 2. The Riemann Integral 3. The Darboux Integral 4. A Functional Zoo 5. Another Approach: Measure Theory 6. The Lebesgue Integral 7. The Gauge Integral 8. Stieltjes-type Integrals and Extensions 9. A Look Back 10. Afterword: L2 Spaces and Fourier Series Appendices: A Compendium of Definitions and Results Index About the Author
SynopsisVarieties 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. This book 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., 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. This book redresses this situation by introducing the Riemann, Darboux, Lebesgue, and gauge integrals using a common set of examples. This 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. With a thorough set of appendices and exercises, and interesting historical context, this book is equally useful as a reference for mathematicians or as a text for a second undergraduate course in real analysis.
LC Classification NumberQA308
