A Treatise on Differential Equations. Supplementary VolumeMacmillan, 1865 - 235 σελίδες |
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Σελίδα 3
... respect to M1 , ma we may affirm that the numerator is the same function of m , as the denominator is of m . Representing these func- tions by ( m ) , ( m , ) respectively , we have u = $ ( m , ) ф ( та ) But m1 , m , being roots of a ...
... respect to M1 , ma we may affirm that the numerator is the same function of m , as the denominator is of m . Representing these func- tions by ( m ) , ( m , ) respectively , we have u = $ ( m , ) ф ( та ) But m1 , m , being roots of a ...
Σελίδα 5
... ( X , Y ̧ ) ( − x ̧ ) ” — r 1.2 ... ( nr ) " + & c . , ........ ( 32 ) the summation extending from n = r to n = ∞o . Forming hence the differential coefficients of A , with respect to ART . 5. ] 5 ADDITIONS TO CHAPTER II . 10.
... ( X , Y ̧ ) ( − x ̧ ) ” — r 1.2 ... ( nr ) " + & c . , ........ ( 32 ) the summation extending from n = r to n = ∞o . Forming hence the differential coefficients of A , with respect to ART . 5. ] 5 ADDITIONS TO CHAPTER II . 10.
Σελίδα 6
George Boole Isaac Todhunter. hence the differential coefficients of A , with respect to x , and yo , and reducing by ( 28 ) , we shall find dA , dA , + f1 ( xo , Yo ) - 0 , dx dy 。 whence in particular dA dA + f1 ( xo , Yo ) = 0 . dx ...
George Boole Isaac Todhunter. hence the differential coefficients of A , with respect to x , and yo , and reducing by ( 28 ) , we shall find dA , dA , + f1 ( xo , Yo ) - 0 , dx dy 。 whence in particular dA dA + f1 ( xo , Yo ) = 0 . dx ...
Σελίδα 26
... respect to dx x , on the above hypothesis as to the constitution of v as a ( dv function of x and u , while is the differential coefficient on the hypothesis that v is reduced to a function of x alone by the conversion of u into a ...
... respect to dx x , on the above hypothesis as to the constitution of v as a ( dv function of x and u , while is the differential coefficient on the hypothesis that v is reduced to a function of x alone by the conversion of u into a ...
Σελίδα 27
... respect to x . Hence the equation re- duces to 0 = Q. And this is not satisfied , since by hypothesis Q does not ... respecting Q , and gives U = f ( x , u ) , we see that if du = f ( x , u ) dx be satisfied by u = 0 , and if at the same ...
... respect to x . Hence the equation re- duces to 0 = Q. And this is not satisfied , since by hypothesis Q does not ... respecting Q , and gives U = f ( x , u ) , we see that if du = f ( x , u ) dx be satisfied by u = 0 , and if at the same ...
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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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