calculus document

May 12th, 2015
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11CalculusKenneth E. IversonCopyright 2002 Jsoftware Inc. All rights reserved.2 CalculusPrefaceCalculus is at once the most important and most difficult subject encountered early bystudents of mathematics; introductory courses often succeed only in turning studentsaway from mathematics, and from the many subjects in which the calculus plays a majorrole.The present text introduces calculus in the informal manner adopted in my Arithmetic [1],a manner endorsed by Lakatos [2], and by the following words of Lanczos from hispreface to [3]:Furthermore, the author has the notion that mathematical formulas have their secretlife behind their Golem-like appearance. To bring out the secret life ofmathematical relations by an occasional narrative digression does not appear to hima profanation of the sacred rituals of formal analysis but merely an attempt to a moreintegrated way of understanding. The reader who has to struggle through a maze oflemmas, corollaries, and theorems, can easily get lost in formalistic details, tothe detriment of the essential elements of the results obtained. By keeping his mindon the principal points he gains in depth, although he may lose in details. The loss isnot serious, however, since any reader equipped with the elementary tools of algebraand calculus can easily interpolate the missing details. It is a well-known experiencethat the only truly enjoyable and profitable way of studying mathematics

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