Theories of Integration The Integrals of Riemann Lebesgue Henstock Kurzweil and McShane 1st Edition by Douglas S Kurtz, Charles W Swartz ISBN 9812388435 9789812388438

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Product details:

ISBN 10: 9812388435

ISBN 13: 9789812388438 

Author: Douglas S. Kurtz, Charles W. Swartz

The book uses classical problems to motivate a historical development of the integration theories of Riemann, Lebesgue, Henstock-Kurzweil and McShane, showing how new theories of integration were developed to solve problems that earlier integration theories could not handle. It develops the basic properties of each integral in detail and provides comparisons of the different integrals. The chapters covering each integral are essentially independent and could be used separately in teaching a portion of an introductory real analysis course. There is a sufficient supply of exercises to make this book useful as a textbook.

Table of contents:

1. Introduction

2. Riemann integral

3. Convergence theorems and the Lebesgue integral

4. Fundamental Theorem of Calculus and the Henstock-Kurzweil integral

5. Absolute integrability and the McShane integral

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Tags: Douglas S Kurtz, Charles W Swartz, Theories of Integration, Integrals, Riemann, Lebesgue, Henstock, Kurzweil, McShane