eBook ISBN:  9781614442097 
Product Code:  DOL/31.E 
List Price:  $35.00 
MAA Member Price:  $26.25 
AMS Member Price:  $26.25 
eBook ISBN:  9781614442097 
Product Code:  DOL/31.E 
List Price:  $35.00 
MAA Member Price:  $26.25 
AMS Member Price:  $26.25 

Book DetailsDolciani Mathematical ExpositionsVolume: 31; 2007; 281 ppMSC: Primary 26; Secondary 28
The derivative and the integral are the fundamental notions of calculus. Though there is essentially only one derivative, there is a variety of integrals, developed over the years for a variety of purposes, and this book describes them. No other single source treats all of the integrals of Cauchy, Riemann, RiemannStieltjes, Lebesgue, LebesgueSteiltjes, HenstockKurzweil, Weiner, and Feynman. The basic properties of each are proved, their similarities and differences are pointed out, and the reason for their existence and their uses are given. There is plentiful historical information. The audience for the book is advanced undergraduate mathematics majors, graduate students, and faculty members. Even experienced faculty members are unlikely to be aware of all of the integrals in the Garden of Integrals and the book provides an opportunity to see them and appreciate their richness. Professor Burk's clear and wellmotivated exposition makes this book a joy to read. The book can serve as a reference, as a supplement to courses that include the theory of integration, and a source of exercises in analysis. There is no other book like it.

Table of Contents

Chapters

Chapter 1. An Historical Overview

Chapter 2. The Cauchy Integral

Chapter 3. The Riemann Integral

Chapter 4. The Riemann–Stieltjes Integral

Chapter 5. Lebesgue Measure

Chapter 6. The Lebesgue Integral

Chapter 7. The Lebesgue–Stieltjes Integral

Chapter 8. The Henstock–Kurzweil Integral

Chapter 9. The Wiener Integral

Chapter 10. The Feynman Integral


Reviews

This book provides a stimulating panorama of the integrals of Cauchy, Riemann, RiemannStieltjes, Lebesgue, LebesgueStieltjes, HenstockKurzweil, Wiener and Feynman. Each argument is well presented and the main properties are displayed. The book is pleasant to read and can serve as a good reference.
B. Bongiorno, Mathematical Reviews


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The derivative and the integral are the fundamental notions of calculus. Though there is essentially only one derivative, there is a variety of integrals, developed over the years for a variety of purposes, and this book describes them. No other single source treats all of the integrals of Cauchy, Riemann, RiemannStieltjes, Lebesgue, LebesgueSteiltjes, HenstockKurzweil, Weiner, and Feynman. The basic properties of each are proved, their similarities and differences are pointed out, and the reason for their existence and their uses are given. There is plentiful historical information. The audience for the book is advanced undergraduate mathematics majors, graduate students, and faculty members. Even experienced faculty members are unlikely to be aware of all of the integrals in the Garden of Integrals and the book provides an opportunity to see them and appreciate their richness. Professor Burk's clear and wellmotivated exposition makes this book a joy to read. The book can serve as a reference, as a supplement to courses that include the theory of integration, and a source of exercises in analysis. There is no other book like it.

Chapters

Chapter 1. An Historical Overview

Chapter 2. The Cauchy Integral

Chapter 3. The Riemann Integral

Chapter 4. The Riemann–Stieltjes Integral

Chapter 5. Lebesgue Measure

Chapter 6. The Lebesgue Integral

Chapter 7. The Lebesgue–Stieltjes Integral

Chapter 8. The Henstock–Kurzweil Integral

Chapter 9. The Wiener Integral

Chapter 10. The Feynman Integral

This book provides a stimulating panorama of the integrals of Cauchy, Riemann, RiemannStieltjes, Lebesgue, LebesgueStieltjes, HenstockKurzweil, Wiener and Feynman. Each argument is well presented and the main properties are displayed. The book is pleasant to read and can serve as a good reference.
B. Bongiorno, Mathematical Reviews