Series In Real Analysis

2 primary works

Theories Of Integration: The Integrals Of Riemann, Lebesgue, Henstock-kurzweil, And Mcshane

by Charles W Swartz and Douglas S Kurtz

Published 4 June 2004

This book presents 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 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 can be used separately in teaching a portion of an introductory course on real analysis. There is a sufficient supply of exercises to make the book useful as a textbook.

Theories Of Integration: The Integrals Of Riemann, Lebesgue, Henstock-kurzweil, And Mcshane (2nd Edition)

by Charles W Swartz and Douglas S Kurtz

Published 2 November 2011

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.