A Treatise on Differential Equations. Supplementary Volume |
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Page xii
... PARTIAL DIFFER ENTIAL EQUATIONS OF THE FIRST ORDER , AND ON Asso- CIATED SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS XXVI . HOMOGENEOUS SYSTEMS OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS XXVII . OF NON - LINEAR PARTIAL DIFFERENTIAL ...
... PARTIAL DIFFER ENTIAL EQUATIONS OF THE FIRST ORDER , AND ON Asso- CIATED SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS XXVI . HOMOGENEOUS SYSTEMS OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS XXVII . OF NON - LINEAR PARTIAL DIFFERENTIAL ...
Page 59
... . Art . 4. ] 2. As it has been shewn that a primitive u = $ ( v ) leads to a linear partial differential equation of the form Pp Qq = R .... ( 1 ) ( 2 ) , provided that u = a , v = b , ART . 2. ] ADDITIONS TO CHAPTER XIV . 59.
... . Art . 4. ] 2. As it has been shewn that a primitive u = $ ( v ) leads to a linear partial differential equation of the form Pp Qq = R .... ( 1 ) ( 2 ) , provided that u = a , v = b , ART . 2. ] ADDITIONS TO CHAPTER XIV . 59.
Page 60
... differential equations dx dy dz = = P Q R . ( 3 ) , it is evident that we shall obtain a solution of the partial dif- ferential equation ( 2 ) by constructing the system of ordinary differential equations ( 3 ) , deducing their general ...
... differential equations dx dy dz = = P Q R . ( 3 ) , it is evident that we shall obtain a solution of the partial dif- ferential equation ( 2 ) by constructing the system of ordinary differential equations ( 3 ) , deducing their general ...
Page 61
... differential equations dx dy dz = P Q R deduce their general integrals in ... equations of the first order , without regard to the number of the variables ... partial differential equation obtained by eliminating dz , dx , dx ,, ... dx ...
... differential equations dx dy dz = P Q R deduce their general integrals in ... equations of the first order , without regard to the number of the variables ... partial differential equation obtained by eliminating dz , dx , dx ,, ... dx ...
Page 63
George Boole Isaac Todhunter. These equations in their developed expression du ... equation - pndxn - p1dx1 + p2dx , ... + P1dx , dz = 0 , and eliminating the differentials , we find X1 P1 + X 2 P2 + Xn ? n = R 2 for the partial differential ...
George Boole Isaac Todhunter. These equations in their developed expression du ... equation - pndxn - p1dx1 + p2dx , ... + P1dx , dz = 0 , and eliminating the differentials , we find X1 P1 + X 2 P2 + Xn ? n = R 2 for the partial differential ...
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Algebra arbitrary constants Calculus of Variations Cambridge Chap Chapter Christ's College cloth College complete primitive condition Conic Sections contains 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 du₂ dx dx dx dy dx₁ dx² dy dp dy dx dy dy dy dz dz dy dz dz eliminate English equa expression Extra fcap factor fcap function Geometry given equation Grammar Hence homogeneous function Last Multiplier Latin linear partial differential m₁ Mathematical method ordinary differential equations Owens College P₁ partial differential equations particular integral Professor Boole proposition reduced relation represent result Schools Second Edition singular solution theorem theory tion transformation Trigonometry u₁ values vanish x₁ Y₁ аф
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