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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from ...Show synopsisThis 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. 1904 Excerpt: ...and y' we get x'Fx.x. + y'Fy.x. = 0, x'Fx.y. + y'F, .y. = 0; hence if x' and y' are not both zero, Fx.x.: Fx.y.: Fy.y. = y" -x'y' x'2; (11) there exists therefore a function 1F of x, y, x, y' such that F x. = y'2Ft, Fx.y. =-x'y'F, Fy.y. = x"F, . (Ha) The function Fx thus defined is of class C in the domain, even when one of the two variables x', y' is zero; but Fl becomes in general infinite when x' and y vanish simultaneously, even if F itself should remain finite and continuous for x'--O, y' = 0. For instance: F = yV/x" + y," F1=.. (l x 2 + y 2) c) Definition of a Minimum: Two points A(x0, y0) and B(xu?/i) being given in the region K, we consider the totality M of all ordinary2 curves which can be drawn in 1R from A to B. Then a curve 6 of M is said to minimize the integral J= I F(x, y, x, y')dt, if there exists a neighborhood H of 6 such that JJ (12) for every ordinary curve 6 which can be drawn in H from A to B. We may, without loss of generality, choose for H the strip3 of the x, ?/-plane swept over by a circle of constant radius p whose center moves along the curve 6 from A to B. This strip will be called "the neighborhood (p) of 6." Compare 3. The definition is due to Weierstrass, Lectures, 1879; compare also Zerhelo, Dissertation, pp. 25-29, and Kneser, Lehrbuch, 17. 2 An extension of the problem to a still more general class of curves will be considered in 31. 3 In case different portions of the strip should overlap, the plane has to be imagined as multiply covered in the manner of a Riemanu-surf ace (weierstrass). h being the second constant of integration. The extremals are therefore cycloids' generated by a circle of radius r rolling upon the horizontal line y--y0+k = 0. To these two equ...Hide synopsis
Description:Good. Shipped within 24 hours. 100% Refund Guaranteed. Ex...Good. Shipped within 24 hours. 100% Refund Guaranteed. Ex-library book-has normal wear and may have library markings/attachments.
Description:Good. Shows some signs of wear, and may have some markings on...Good. Shows some signs of wear, and may have some markings on the inside. Shipped to over one million happy customers. Your purchase benefits world literacy!
Description:Good. Shows some signs of wear, and may have some markings on...Good. Shows some signs of wear, and may have some markings on the inside. Shipped to over one million happy customers. Your purchase benefits world literacy!
Description:Very Good. 1960 Hardcover Second Edition. Former Library book....Very Good. 1960 Hardcover Second Edition. Former Library book. Great condition for a used book! Minimal wear. Shipped to over one million happy customers. Your purchase benefits world literacy!
Description:Very Good. 1960 Hardcover Second Edition. Former Library book....Very Good. 1960 Hardcover Second Edition. Former Library book. Great condition for a used book! Minimal wear. Shipped to over one million happy customers. Your purchase benefits world literacy!
Description:Acceptable. This is a 1961 unabridged and corrected...Acceptable. This is a 1961 unabridged and corrected republication of the original 1904 edition. Cover well worn and stained. Spine has some damage/wear. Some markings on pages.
Description:Good. 1961 Paperback First illus. 271 p. Former Library book. ...Good. 1961 Paperback First illus. 271 p. Former Library book. "An unabridged and corrected republication of the work first published...in 1904." Shows some signs of wear, and may have some markings on the inside. Shipped to over one million happy customers. Your purchase benefits world literacy!
Description:Good. 1961 Paperback First illus. 271 p. Former Library book. ...Good. 1961 Paperback First illus. 271 p. Former Library book. "An unabridged and corrected republication of the work first published...in 1904." Shows some signs of wear, and may have some markings on the inside. Shipped to over one million happy customers. Your purchase benefits world literacy!
Description:Very Good in Unknown jacket. Very Good in Unknown jacket Very...Very Good in Unknown jacket. Very Good in Unknown jacket Very Good 8vo-over 7¾"-9¾" tall Paperback, 271 pp. Edge wear, else clean throughout.
Description:Paperback, some underlining and margin notes, has edge wear to...Paperback, some underlining and margin notes, has edge wear to corners and edges. INV#H-35 G/no DJ.
