Concrete Mathematics: A Foundation for Computer Science (1st by Donald E. Knuth, Ronald L. Graham, Oren Patashnik

By Donald E. Knuth, Ronald L. Graham, Oren Patashnik

This e-book introduces the maths that help complicated desktop programming and the research of algorithms. The book's fundamental objective is to supply an exceptional and correct base of mathematical abilities. it really is an fundamental textual content and reference for computing device scientists and critical programmers in nearly each self-discipline.

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Extra info for Concrete Mathematics: A Foundation for Computer Science (1st Edition)

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Such considerations motivate the following manipulations. We have Sq = x CljClk l

1 l/6 = 55. Incidentally, page 72 of the CRC Tables has further information about the sums of cubes, . . , tenth powers. The definitive reference for mathematical formulas is the Handbook of Mathematical Functions, edited by Abramowitz and Stegun [2]. 38), together with the analogous formulas for sums of cubes, . . , fifteenth powers, with or without alternating signs. But the best source for answers to questions about sequences is an amazing little book called the Handbook of Integer Sequences, by Sloane [270], which lists thousands of sequences by their numerical values.

L. 6 FINITE AND INFINITE CALCULUS 49 example, C might be the periodic function a + b sin2nx; such functions get washed out when we take differences, just as constants get washed out when we take derivatives. At integer values of x, the function C is constant. Now we’re almost ready for the punch line. Infinite calculus also has definite integrals: If g(x) = Df(x), then /‘g(x)dx = f(x)11 = f(b) -f(a). a Therefore finite calculus-ever mimicking its more famous cousin- has definite Sims: If g(x) = Af(x), then Lb g(x) 6x = f(x)i’ = f(b) -f(a).

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