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CALCULUS AND THE RACE TRACK PRINCIPLE
Calculus and Mathematica (C&M) by Davis, Porta and Uhl ia a well thought-out method that, when used properly, gives students an intuitive understanding of, and a feeling for, all the major calculus concepts. It is comprised of the following four books: C&M / Derivatives, C&M / Integrals, C&M / Vector Calculus, and C&M / Approximation, known also as Books 1-4. In these books the authors advocate an explore-and-discover method for teaching the basic concepts of Calculus to undergraduate students. As indicated by the title of this series of books, Mathematica facilitates the exploration. One of the most astonishing thing encountered in Books 1, 2, and 4 is the use of the race track principle. This little known principle is elegantly used to prove or explain just about anything. Below we show examples of how this principle is used - to explain the round-off errors that appear in, say, handheld - to prove the second fundamental theorem of integration, and - to explain the series expansion of a function.
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