Varieties of Integration (Hardcover)
 
作者: C Ray Rosentrater 
書城編號: 1090149


售價: $476.00

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出版社: Cambridge University Press
出版日期: 2016/02/23
尺寸: 228x152x23mm
重量: 570 grams
ISBN: 9780883853597

商品簡介
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.
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