Treatise on Differential EquationsMacmillan, 1865 |
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Resultat 1-5 av 19
Side 26
... dv ( dv ) dx dv dv du = + dx du dx ' in which is the differential coefficient of v with respect to dx x , on the above hypothesis as to the constitution of v as a ( dv dx function of x and u , while is the differential coefficient on ...
... dv ( dv ) dx dv dv du = + dx du dx ' in which is the differential coefficient of v with respect to dx x , on the above hypothesis as to the constitution of v as a ( dv dx function of x and u , while is the differential coefficient on ...
Side 60
... dv dv + Q dx + R = dy dz which must be identically satisfied . Eliminating P , Q , R from these three equations 60 [ CH . XXIV . ADDITIONS TO CHAPTER XIV .
... dv dv + Q dx + R = dy dz which must be identically satisfied . Eliminating P , Q , R from these three equations 60 [ CH . XXIV . ADDITIONS TO CHAPTER XIV .
Side 116
... dv d dp dx dv dP du Hence since is the coefficient of in 116 NON - LINEAR PARTIAL DIFFERENTIAL [ CH . XXVII .
... dv d dp dx dv dP du Hence since is the coefficient of in 116 NON - LINEAR PARTIAL DIFFERENTIAL [ CH . XXVII .
Side 117
... dv A dx ; du A ' ; dx ; du d2v du d2v dv d2u dv d2u or Σ i = n or or + dx dpdx , dp , dxdxdx , dpdx , dp , dxdx , - du dv d Σ du dv dx ; d dx dp dx , [ uv ] , dp dx ; In like manner the coefficient of - d dp , [ uv ] . dP is dx ; Hence ...
... dv A dx ; du A ' ; dx ; du d2v du d2v dv d2u dv d2u or Σ i = n or or + dx dpdx , dp , dxdxdx , dpdx , dp , dxdx , - du dv d Σ du dv dx ; d dx dp dx , [ uv ] , dp dx ; In like manner the coefficient of - d dp , [ uv ] . dP is dx ; Hence ...
Side 121
... dv dv + dF / du dv \ dx + dz P + du du du + 2+ s + du dy dz dp dq dv dv r + = dp = 0 , + dv dy dz dF / dv dv + q + dv dv s + t = 0 . dp dq For brevity , write du du for du dx dx + P dz and ( dy ) for dy + 9 de du dz ' and then eliminating ...
... dv dv + dF / du dv \ dx + dz P + du du du + 2+ s + du dy dz dp dq dv dv r + = dp = 0 , + dv dy dz dF / dv dv + q + dv dv s + t = 0 . dp dq For brevity , write du du for du dx dx + P dz and ( dy ) for dy + 9 de du dz ' and then eliminating ...
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A Treatise on Differential Equations: Supplementary Volume George Boole Uten tilgangsbegrensning - 1865 |
Vanlige uttrykk og setninger
arbitrary constants C₂ Cambridge Chap Chapter complete primitive condition Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dp dFdF differential coefficients dp dF dp dp dx dp dq dp dy dq dp du₁ dv dv dx dp dx dx dx dy dy dx dz dx₁ dx² dy dq dy dx dy dz dz dy dz dz Edition eliminate equa Eton College expression Extra fcap factor Fcap given equation Hence homogeneous function J. P. MAHAFFY Jacobi John's College Last Multiplier LATIN linear partial differential m₁ numerous ordinary differential equations Owens College P₁ partial differential equations particular integral Professor Boole reduced represent result shewn singular solution system of ordinary theorem theory tion transformation Trinity College u₁ u₂ values vanish whence X₁ y₁ аф