Mathematics By Martin Gardner, Silvanus P. Thompson

ISBN-10: 0312185480

ISBN-13: 9780312185480

Calculus Made Easy has lengthy been the preferred calculus primer, and this significant revision of the vintage math textual content makes the topic handy nonetheless extra understandable to readers of all degrees. With a brand new creation, 3 new chapters, modernized language and strategies all through, and an appendix of demanding and stress-free perform difficulties, Calculus Made Easy has been completely up to date for the trendy reader.

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Extra info for Calculus Made Easy

Sample text

Note that the series beyond 2 is the same as the original halving series which we took as x. This enables us to substitute x for the sequence and write 2x = 2 + x. Rearranging terms to 2x - x = 2 gives x, the limit of the series, a value of 2. The same trick will show that is the limit of + ~ + + -dr + .... ; it works on any series in which terms decrease in • geometnc progressIOn. Bouncing ball problems are common in the literature on limits. They assume that an ideally elastic ball is dropped a specified distance to a hard floor.

Let's start with Zeno's runner. Assume that he runs ten meters per second on a path from zero to 100 meters. The independent variable is time, represented by the x axis of a Cartesian graph. The dependent variable y is the runner's distance from his starting spot. It is represented on the y axis. Because the function is linear, the runner's motion graphs as an upward tilted straight line from zero, the graph's origin, to the point that is ten seconds on the time axis and 100 meters on the distance axis.

E num er e you WI encounter It in Thompson's Chapter 14) is the limit of 1 + f. + ~ + + i. 1 4! tr + ..... 26 CALCULUS MADE EASY Although Archimedes did not know calculus, he anticipated integration by calculating pi as the limit of the perimeters of regular polygons as their number of sides increases. In the language of infinitesimals, a circle can be viewed as the perimeter of a regular polygon with an infinity of sides, its perimeter consisting of an infinity of straight line segments each of infinitesimal length.