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    3. Analysis by Its History [Repost]

    Analysis by Its History [Repost]

    Posted By: metalero87
    Date: 13 Sep 2014 20:29:36
    Analysis by Its History [Repost]

    "Analysis by Its History" by Hairer
    2008 | ISBN: 0387770313 | Pages: 389 | English | PDF | 12 MB

    This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.
    Reader's review:
    This books gives a unique approach to Calculus using its historical development. The most notable feature of the book is that the order of topics is reversed from what has become standard in current textbooks. It begins with the analysis of areas and volumes. This is followed by derivatives, continuity, and the notion of function. This is the order in which analysis developed, but not the order one would follow if building understanding of the subject from a foundation upward. Historically, the foundations were laid last.

    The book is not intended as a history of analysis. It is rather intended as a textbook or reference in which the topics are presented in historical order. The historical background is intended to give insight into a modern view of the subject. It accomplishes this admirably.

    The book is filled with examples, quotes, vignettes, historical background, computer graphics, and copies of original documents. Special topics are interspersed throughout. The book gives us a fresh and envigorating view of Calculus. It is an invaluable resource.

    UPWARDS