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Analysis by Its History (Undergraduate Texts in Mathematics)

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Analysis by Its History (Undergraduate Texts in Mathematics)

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    Available in PDF Format | Analysis by Its History (Undergraduate Texts in Mathematics).pdf | English
    Ernst Hairer(Author) Gerhard Wanner(Author)

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 quotationsare 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 wellas researchers.

"...well done, attractively designed...And above all, it proposes an interesting approach to teaching analysis." Internationale Mathematische Nachrichten

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  • By A. White on 5 October 2009

    This is an excellent book, though perhaps for a somewhat restricted readership.Long, long ago I knew the material they present. Nevertheless, reading Hairer and Wanner's historical approach I really "got" for the very first time what an extraordinary intellectual and human achievement calculus-analysis is. I liked the clarity applied to describing the non-rigourous C17 methods; in particular I enjoyed seeing both how much and how little had been achieved in the 17th century before Newton/Leibniz. I enjoyed seeing how the powerful C17 techniques were slowly underpinned, over 200 years, by subtle reasoning about the real line. The book is richly illustrated with concrete examples and is interesting and lucid.But who is the intended reader? Though it covers textbook subjects, the expository style is fairly mature, and this is not a textbook for beginners. And though it goes in historical order it's not a history book, and you'd still need to read one of those. It will be an excellent resource for teachers at all levels from school upwards; as a background resource for undergraduates; for those who want a more rigorous account of these parts of mathematical history than the history books give; for those who know at least some calculus and want to educate themselves in analysis; for those who know a lot, but want the clarity of the historical overview. For any of those I strongly recommend this excellent book.

  • By Prof Dr Thomas Sonar on 27 September 2009

    and classroom-tested! Hairer and Wanner give a great introduction to mathematical analysis along the lines of its discovery. The binomial theorem appears fairly early and shows itself as THE powerful centre of analysis. I used this book twice in courses on analysis and it never let me down. All proofs are correct; at every point we find clear, historically important proofs instead of the most elegant ones. This book ist a "must have" and should have its place on every book shelf.

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