A Garden of Integrals (Dolciani Mathematical Expositions) by Frank Burk (PDF)

Description

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 reasons for their existence and their uses are given, with plentiful historical information. The audience for the book is advanced undergraduate mathematics students, graduate students, and faculty members, of which even the most experienced are unlikely to be aware of all of the integrals in the Garden of Integrals. Professor Burk’s clear and well-motivated exposition makes this book a joy to read. There is no other book like it.

User’s Reviews

Editorial Reviews: Review 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 Book Description Burk proves the basic properties of various integrals, draws comparisons and analyses their uses. Book Description Though there is essentially only one derivative, there is a variety of integrals. In this book the basic properties of each are proved, their similarities and differences are pointed out, and the reasons for their existence and their uses are given. There is no other book like it. From the Inside Flap 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 the richness of the idea of integral. Professor Burke’s clear and well-motivated exposition makes this book a joy to read. The book can serve as a reference, as a supplement to course that include the theory of integration, and a source of exercises in analysis. There is no other book like it. About the Author Frank Burk was Professor Emeritus at the California State University in Chico before his death in March 2007. Read more

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