Varieties of integration / C. Ray Rosentrater, Westmont College.

Format:

Book

Author/Creator:

Rosentrater, C. Ray, author.

Series:

Dolciani mathematical expositions ; no. 51.

Dolciani Mathematical Expositions, v. 51

Language:

English

Subjects (All):

Integrals.

Calculus, Integral.

Physical Description:

1 online resource (xv, 325 pages)

Place of Publication:

Washington, DC : Mathematical Association of America, [2015]

System Details:

Mode of access : World Wide Web

Summary:

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.-- Publisher.

Contents:

Preface Chapter 1. Historical Introduction Chapter 2. The Riemann Integral Chapter 3. The Darboux integral Chapter 4. A Functional zoo Chapter 5. Another Approach: Measure Theory Chapter 6. The Lebesgue Integral Chapter 7. The Gauge Integral Chapter 8. Stieltjes-type Integrals and Extensions Chapter 9. A Look Back Chapter 10. Afterword: $L_2$ Spaces and Fourier Series Appendices: A Compendium of Definitions and Results

Notes:

Includes bibliographical references and index.

Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2015

Description based on print version record.

Other Format:

Print version: Rosentrater, C. Ray, Varieties of integration /

ISBN:

9781614442172 (online)

Access Restriction:

Restricted for use by site license.