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" ... the first with respect to x, and the second with respect to y. Similarly we put J2 du , d?u ~dx  "
A Treatise on the Differential and Integral Calculus: And on the Calculus of ... - Page 112
by Edward Henry Courtenay - 1855 - 501 pages
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A Treatise on the Differential and Integral Calculus: And on the Calculus of ...

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...
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A Treatise on the Differential and Integral Calculus: And on the Calculus of ...

Edward Henry Courtenay - Calculus - 1857 - 522 pages
...rf^TT2"I"'" <M But we put for convenience — 5 — = , indicating thereby that two differentiations of »t have been performed, the first with respect to x,...the second with respect to y. Similarly we put J2 du J tPu ~dx d2u 1c2 d?u and — ; — = -,—; — ; the first expression indi, , , , o . — ; — --,—;...
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A Treatise on the Differential and Integral Calculus: And on the Calculus of ...

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...
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A Treatise on the Differential and Integral Calculus: And on the Calculus of ...

Edward Henry Courtenay - Calculus - 1873 - 528 pages
...dx TT ЬУ À? du dx сРи oPu (fju ~dx3 k "~dx3 But we put for convenience du , indicating thereby dy dxdy that two differentiations of u have been performed,...and the second with respect to y. Similarly we put Tx n3 llj;~ u"tt. . , „ — : , , „ , and — -— = , „ , : the first expression nidii/y2 dxdy2...
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A Treatise on the Differential and Integral Calculus: And on the Calculus of ...

Edward Henry Courtenay - Calculus - 1873 - 524 pages
...<Pa <?« . <fju , ~d72 k ~d7> F <e <« But we put for convemence — - — = yr- , indicating thereby that two differentiations of u have been performed, the first with respect to .T, and the second with respect to y. Similarly we put _ du , d2u d2 — d — dx iPu d*- d2!/ , ....
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Uniplanar Kinematics of Solids and Fluids: With Applications to the ...

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)...
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Applied Complex Variables

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 =...
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Computational Mathematics in Engineering and Applied Science: ODEs, DAEs ...

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...
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Computational Science and Its Applications - ICCSA 2004 ..., Part 2

Antonio Laganà, Marina L. Gavrilova, Vipin Kumar, Youngsong Mun, C.J. Kenneth Tan, Osvaldo Gervasi - Computers - 2004 - 1446 pages
...with a product of two small perturbations, to find ut+vop¿=O and P¿+(Jux0. fc2\ \vo/ Differentiate the first with respect to x, and the second with respect to t. Multiply the first by c 2 /vo and subtract the result from the second, to find — c¿13¿ = 0....
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Numerical Solution of Partial Differential Equations in Science and Engineering

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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