ISBN: 113050350X

[EAN: 9781130503500], Nieuw boek, [SC: 13.4], [PU: RareBooksClub], GEORGE WIRGMAN HEMMING,WORLD, This item is printed on demand. Paperback. 42 pages. Dimensions: 9.7in. x 7.4in. x 0.1in.T… Mehr…

[EAN: 9781130503500], Nieuw boek, [SC: 13.4], [PU: RareBooksClub], GEORGE WIRGMAN HEMMING,WORLD, This item is printed on demand. Paperback. 42 pages. Dimensions: 9.7in. x 7.4in. x 0.1in.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. 1852 Excerpt: . . . x Ax, the above expression becomes ( Ax, y Ay)-(x Ax, y) j and Ax is the difference between these two values: dy. . , which by the definition --ltJAyjyA, y) It(Myy)-f(x, y)). Ax J (x Ax, y Ay)-f(x Ax, y)-(x, y Ax) (x, y)-wa0 I AxA writing Uia because it appears by the previous step that the limitsare to be taken by making both Ax and Ay approach zero. The value of may be found in the same way, and will be precisely the same as that of Jx since the above expression (being perfectly symmetrical) remains unaltered when x and y are interchanged. dx dy and the symbol, f(x, y) may be used to denote either of them. Cor. 1. If x and y are independent variables, we obtain from the above equation, since dx, dy are constant, dxdy dxdy In this case therefore, djdju-dft, u. It must be remembered that this equation does not hold, unless x and y are independent variables. Cor. 2. From the equation ----it is easily seen that when a function is to be differentiated m times partially with respect to one variable, and n times with respect to another, the order in which the differentiations are performed is immaterial; for by repeatedly interchanging any two contiguous symbols (by virtue of the above theorem) the order may evidently be changed in any manner we please. 138. On the notations employed to represent successive partial differentials and differential coefficients. Having employed du, dau to represent the partial differentials of u with respect to x and y, the successive partial differentials must, consistently with our notation in the case of functions of one independent variable, be represented by dji, dju dju, dyu, du du, dju dxmdyu (1), and representing the partial differential coefficients of u or F(x, y) by F(x) an. . . This item ships from La Vergne,TN.<

2012, ISBN: 113050350X

[EAN: 9781130503500], Nieuw boek, [SC: 2.64], [PU: Rarebooksclub.com, United States], Language: English Brand New Book ***** Print on Demand *****.This historic book may have numerous typ… Mehr…

[EAN: 9781130503500], Nieuw boek, [SC: 2.64], [PU: Rarebooksclub.com, United States], Language: English Brand New Book ***** Print on Demand *****.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. 1852 Excerpt: .x + Ax, the above expression becomes /( + Ax, y + Ay)-/(x + Ax, y) j and Ax is the difference between these two values: dy. ., which by the definition =--ltJA+y+jyA, y) It(My+y)-f(x, y)). Ax J //(x + Ax, y + Ay)-f(x + Ax, y)-/(x, y + Ax) +/(x, y)-wa=0 I AxA / writing Ui a because it appears by the previous step that the limitsare to be taken by making both Ax and Ay approach zero. The value of may be found in the same way, and will be precisely the same as that of Jx since the above expression (being perfectly symmetrical) remains unaltered when x and y are interchanged. dx dy and the symbol, f (x, y) may be used to denote either of them. Cor. 1. If x and y are independent variables, we obtain from the above equation, since dx, dy are constant, dxdy dxdy In this case therefore, djdju-dft, u. It must be remembered that this equation does not hold, unless x and y are independent variables. Cor. 2. From the equation =----it is easily seen that when a function is to be differentiated m times partially with respect to one variable, and n times with respect to another, the order in which the differentiations are performed is immaterial; for by repeatedly interchanging any two contiguous symbols (by virtue of the above theorem) the order may evidently be changed in any manner we please. 138. On the notations employed to represent successive partial differentials and differential coefficients. Having employed du, dau to represent the partial differentials of u with respect to x and y, the successive partial differentials must, consistently with our notation in the case of functions of one independent variable, be represented by dji, dju dju, dyu, d u du, dju dxmdy u (1), and representing the partial differential coefficients of u or F(x, y) by F (x) an.<