Conceived by the author as an introduction to "why the calculus works," this volume offers a 4-part treatment: an overview; a detailed examination of the infinite processes arising in the realm of numbers; an exploration of the extent to which familiar geometric notions depend on infinite processes; and the evolution of the concept of functions. 1982 edition.
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Gardiner (U. of Birmingham) writes for undergraduate and high school students, and general readers with some mathematical background. He explains why the calculus works, and emphasizes the critical need for precision when dealing with infinite mathematics. The 1982 edition was published by Springer-Verlag with the subtitle Background to Analysis ,
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