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A Garden of Integrals
 
A Garden of Integrals
MAA Press: An Imprint of the American Mathematical Society
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
A Garden of Integrals
Click above image for expanded view
A Garden of Integrals
MAA Press: An Imprint of the American Mathematical Society
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 Details
     
     
    Dolciani Mathematical Expositions
    Volume: 312007; 281 pp
    MSC: 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 312007; 281 pp
MSC: 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.

  • 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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