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Theory of Maxima and Minima

Theory of Maxima and Minima


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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. 1917 edition. Excerpt: ...i=l If, then, y is a linear function of the x's having the form 21 y = c1x1 + c2x2 H h cnxn, and if g is a certain constant, then the expression f--gy2(=l, say), after the theorem proved above, can be expressed as a function of only n--1 variables if the constants kv k2, kH may be so determined that = n A = n A=l A = l or 22 a-xca=0. A=l A=l From the assumption made regarding 20 it follows, on the one hand, that the inequality 23 0 A must exist. This is the only restriction placed upon the c's. On the other hand, in virtue of the n linear equations 24 AA=tfA (X=l,2, ..., n) See also Lagrange, Misc. Taur., Vol. I (1759), p. 18, and Micanique, Vol. I, p. 3; Gauss, Dixq. Arithm., p. 271: Theoria Comb. Observ., p. 31, etc. the quantities xv xv, xn may be expressed as linear functions of fv f2, fn, and, consequently, by the substitution of these values of xv xv., xn in 21 y takes the form where the e are constants, which are composed of the constants But from equation 22 it follows that 1 y =-_. 9 Such a representation of the 4, however, since we have to do with linear equations, can be effected only in one way. Comparing this result with 21, we have 27 c =, (-i, ev., --) (- = 1. 2., -). and consequently 28 =; A = l or, from 18, g = (-!, -2', e-) Since the quantities cv c2, cn are perfectly arbitrary except the one restriction expressed by the inequality 23, the quantities ev %, en are, m consequence of the equation 27, completely arbitrary with the one limitation resulting from 28, viz., the function f cannot vanish for the system of values (ev e2, en); otherwise g would become infinite. 57. Eeciprocally, if the quantities ev ev, en are arbitrarily chosen, but with the...


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Product Details
  • ISBN-13: 9781154869361
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 50
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1154869369
  • Publisher Date: 01 Jul 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 109 gr


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