Varieties of Integration
£33.99
Part of Dolciani Mathematical Expositions
- Author: C. Ray Rosentrater, Westmont College, California
- Date Published: February 2016
- availability: Available in limited markets only
- format: Hardback
- isbn: 9780883853597
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Hardback
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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.
Read more- An historically motivated, cohesive survey of the most common types of integration
- Unifies some seemingly disparate frameworks for integration using a common set of examples
- Pedagogy is a clear priority, and the different types of integration are compared in multiple enlightening ways
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×Product details
- Date Published: February 2016
- format: Hardback
- isbn: 9780883853597
- length: 330 pages
- dimensions: 236 x 156 x 23 mm
- weight: 0.57kg
- availability: Available in limited markets only
Table of Contents
Preface
1. A 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.
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