eBook ISBN: | 978-1-61444-209-7 |
Product Code: | DOL/31.E |
List Price: | $35.00 |
MAA Member Price: | $26.25 |
AMS Member Price: | $26.25 |
eBook ISBN: | 978-1-61444-209-7 |
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, Riemann-Stieltjes, Lebesgue, Lebesgue-Steiltjes, Henstock-Kurzweil, 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 well-motivated 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, Riemann-Stieltjes, Lebesgue, Lebesgue-Stieltjes, Henstock-Kurzweil, 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
-
-
RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Reviews
- Requests
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, Riemann-Stieltjes, Lebesgue, Lebesgue-Steiltjes, Henstock-Kurzweil, 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 well-motivated 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, Riemann-Stieltjes, Lebesgue, Lebesgue-Stieltjes, Henstock-Kurzweil, 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