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1. Mathematical Tables

1. Mathematical Tables


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About the Book

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1916 Excerpt: ...Xl = U + V and x2--u--v are roots of the equation. (2) To solve o cos x--& sin x = c, where o and 6 are positive: Find u and r as above. Then xj =--(u + v) and x2 =--(u--v) are roots of the equation. General Method of Solution by Trial and Error. This method is applicable to a numerical equation of any form, and can be carried out to any desired degree of approximation. It is especially useful when a: first approximation to a root is already known. Write the equation in the form /(x) = 0, where /(x) means any function of x, and plot the curve y = f(x) for a sufficient number of values of x to obtain a general idea of the shape of the curve. Then pick out the regions in which the curve appears to cross the axis of x, and plot the curve more accurately in each of these regions. Thus, by successive approximations, plotting the important parts of the curve on a larger and larger scale, determine as accurately as necessary the points where the curve crosses the axis--that is, the values of x which make/(x) equal to zero. Thus, suppose that f(x) = 3.0 when x = 2.6 and--5.0 when x = 2.7 (see Fig. 1). Then the curve must cross the axis somewhere between x = 2.6 and x = 2.7; and since it will not vary greatly from a straight line between those points, it is seen that it must Fio. 1. cross near 2.64. Suppose the value of f(x) when computed for x = 2.64, is--0.2, and when computed for x = 2.63 is + 0.7; then the root lies between x = 2.63 and 2.64. Plotting this section on the larger scale, it is seen that the next guess should be about 2.638; and so on. Instead of writing the original equation with all the terms on the left-hand side, it is often better to divide the expression into two parts, say /i(x) and/2(x), writing the equation in the form/i(x) = /2(x). If ...


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Product Details
  • ISBN-13: 9781130984842
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 46
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1130984842
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 100 gr


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