Titlebook: Calculus Made Easy; Silvanus P. Thompson,Martin Gardner Textbook Nov 1999Latest edition Macmillan Publishers Limited 1998

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對待

What Is a Derivative?In Chapter 3 Thompson makes crystal clear what a derivative is, and how to calculate it. However, it seemed to me useful to make a few introductory remarks about derivatives that may make Thompson’s chapter even easier to understand.

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To Deliver You from the Preliminary TerrorsThe preliminary terror, which chokes off most high school students from even attempting to learn how to calculate, can be abolished once for all by simply stating what is the meaning—in common-sense terms—of the two principal symbols that are used in calculating.

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都相信我的話

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Sums, Differences, Products, and QuotientsWe have learned how to differentiate simple algebraical functions such as . + . or ., and we have now to consider how to tackle the . of two or more functions.

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Successive DifferentiationLet us try the effect of repeating several times over the operation of differentiating a function. Begin with a concrete case.

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Introducing a Useful DodgeSometimes one is stumped by finding that the expression to be differentiated is too complicated to tackle directly.

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漂白

Maxima and MinimaA quantity which varies continuously is said to pass by (or through) a local maximum or minimum value when, in the course of its variation, the immediately preceding and following values are . smaller or greater, respectively, than the value referred to. An infinitely great value is therefore not a maximum value.