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  3. A Garden of Integrals
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    • Publisher:
      Mathematical Association of America
      Publication date:
      05 April 2012
      01 June 2007
      ISBN:
      9781614442097
      9780883853375
      DOI:
      https://doi.org/10.7135/UPO9781614442097
      Dimensions:
      Weight & Pages:
      00kg,
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics, Real and Complex Analysis
      Series:
      Dolciani Mathematical Expositions
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    Subjects:
    Mathematics, Real and Complex Analysis
    Series:
    Dolciani Mathematical Expositions
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    Book description

    The derivative and the integral are the fundamental notions of calculus. Though there is essentially only one derivative, there are 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. Historical information is plentiful. Advanced undergraduate mathematics majors, graduate students, and faculty members are the audience for the book. 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.

    Reviews

    "The underlying theme of the book is the development of the idea of the integral from ancient to modern times. Each of these gets a chapter of its own: the integrals of Cauchy, Riemann, Riemann-Stieltjes, Lebesgue, Lebesgue-Stieltjes, Henstock-Kurtzweil, Wiener, and Feynman. Generally this approach works very well. I can’t think of a comparable book at this level with a scope as broad as this one. ... Once the author begins discussing the individual integrals, he is truly in his element. Most chapters consist of a concise discussion of an integral with a generous number of illustrative examples and exercises."

    William J. Satzer Source: MAA Reviews

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