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 ...
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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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Add this copy of Varieties of Integration (Dolciani Mathematical to cart. $35.96, good condition, Sold by Bulrushed Books rated 5.0 out of 5 stars, ships from Moscow, ID, UNITED STATES, published 2015 by Mathematical Association of America.
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Good. Good or better condition. Pages have scattered marks and notes, but completely legible, binding is good. Covers mostly clean, minor scuffing or stickers. Solid reading copies.
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Add this copy of Varieties of Integration (Dolciani Mathematical to cart. $103.52, new condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2016 by American Mathematical Society.
