Overview

The manuscript gives a coherent and detailed account of the theory of series in the eighteenth and early nineteenth centuries. It provides in one place an account of many results that are generally to be found - if at all - scattered throughout the historical and textbook literature. It presents the subject from the viewpoint of the mathematicians of the period, and is careful to distinguish earlier conceptions from ones that prevail today.

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9786611141509

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From the reviews: <p> Giovanni Ferraroa (TM)s book must be regarded as an important contribution to the history of mathematical analysis a ] . In summary, this book is thoroughly researched; it is written with a high degree of accuracy, and the broad range of fascinating material is, in general, very well organized. Therefore a ] every college and university library should have a copy. In fact, extracts from the book could be used to inject historical perspectives into courses on analysis, and it will certainly appeal to historians in general. (Peter Ruane, MathDL, April, 2008) <p> The work is thoroughly referenced and should prove valuable to mathematical history researchers a ] . Summing Up: Recommended. Researchers/faculty and professionals. (C. Bauer, CHOICE, Vol. 46 (01), September, 2008) <p> The author begins his detailed account with the arrival of the calculus with Newton and Leibniz, and their own treatments of series. a ] The range of series and functions treated is impressive a ] . The story stops with a brief notice of the start of the critical phase, especially concerning the convergence (or not) of infinite series, which was put forward by Cauchy and his followers a ] . The book is a valuable contribution, possibly the single most substantial source on the topic. (I. Grattan-Guinness, Mathematical Reviews, Issue 2008 k)

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