ENGLISH

A Garden of Integrals (Dolciani Mathematical Expositions)

By Frank E. Burk

Book information

Publisher
Mathematical Association of America
Year
2007
ISBN
088385337X, 9780883853375
Open Library ID
OL11232669M
Language
english
Format
PDF
Filesize
11 MB (11360256 bytes)
Pages
296\296
Time added
2011-06-04 13:46:07

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 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 Burks 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.

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