 | Edward Henry Courtenay - Calculus - 1855 - 526 pages
...dy \ dy2 1 . 2 <P« , dtu dx2 k dx2 k2 d^^ ^-+^r'i + "^"iT2 + dy dxdy that two differentiations of u have been performed, the first with respect to x,...the second with respect to y. Similarly we put J2 du , d?u ~dx <Pu ~d72 d*u . ,. and — ; — = . „ , ; the first expression indi2' - = — ; — , —... | |
 | Edward Henry Courtenay - Mathematics - 1856 - 524 pages
...we put for convenience — . — = , , , indicating thereby dy dr.dy that two differentiations of M have been performed, the first with respect to x,...the second with respect to y. . Similarly we put J2 dll , dZU dx d2u dx2 d2M , - = > , , , and — . — = , ,; the first expression mdidy* dxdy2 ' dy... | |
 | Edward Henry Courtenay - Calculus - 1868 - 530 pages
...rfz rf2u But we put for convenience —3 — = , indicating thereby that two differentiations of w have been performed, the first with respect to x, and the second with respect to y. Similarly we put du . d?u d2 — d — dx d3u djc2 rf3« and = ; the first expression indi, „ = , , „, — ; rfy-8... | |
 | George Minchin Minchin - Kinematics - 1882 - 284 pages
...X, (<t — c^\ — 2#2y. (l& dx dv Hence -£ + ~ = 4//- (6) Also by differentiating equations (5), the first with respect to x and the second with respect to y, and substituting for — and -J^-, whenever they occur, their values given in (5), we have Hence (4)... | |
 | John Warren Dettman - Mathematics - 1965 - 514 pages
...Cauchy-Riemann equations are satisfied; that is, uп = cu and и„ = —ип. If we differentiate the first with respect to x and the second with respect to y and add, we have If the second partial derivatives of и and и exist and are continuous then f*v =... | |
 | W.E. Schiesser - Mathematics - 1993 - 604 pages
...tried and found did not work is to compute d^u/dxdy by two successive first-order differentiations, the first with respect to x and the second with respect to y (using subroutine DSS004, for example). This apparently gave an unstable system of ODEs, since initially... | |
 | Leon Lapidus, George F. Pinder - Mathematics - 1982 - 698 pages
...and generate a second-order PDE from two first-order PDEs. Consider », + $»,=0 Differentiation of the first with respect to x and the second with respect to y, multiplication of the second by g, and subtraction yields (g and A are independent of x and v ) u 0... | |
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Eq. (4.7), we may take partial derivatives of the first with respect to x and the second with respect to y and... 