A Treatise on Differential Equations, Volum 1Macmillan, 1872 - 85 sider |
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Resultat 1-5 av 13
Side vii
... operations . I have endeavoured to shew in Chap . XVI . , that the expressions by which these inverse operations are sym- bolized are in reality a species of interrogations , admitting of answers , legitimate , but differing in species ...
... operations . I have endeavoured to shew in Chap . XVI . , that the expressions by which these inverse operations are sym- bolized are in reality a species of interrogations , admitting of answers , legitimate , but differing in species ...
Side 27
... operation , a series of values of y will be deter- mined , only one of which is arbitrary , while all the others are assigned in terms of that arbitrary value and of the known values of x . If , for example , we have the particular ...
... operation , a series of values of y will be deter- mined , only one of which is arbitrary , while all the others are assigned in terms of that arbitrary value and of the known values of x . If , for example , we have the particular ...
Side 42
... ) + df , ( x , y ) ƒ , ( x , y ) . 2 ( 26 ) , And , continuing thus to repeat the same operation , we obtain a series of equations determining the successive differential coefficients of 42 [ CH . II . GENERAL SOLUTION BY DEVELOPMENT .
... ) + df , ( x , y ) ƒ , ( x , y ) . 2 ( 26 ) , And , continuing thus to repeat the same operation , we obtain a series of equations determining the successive differential coefficients of 42 [ CH . II . GENERAL SOLUTION BY DEVELOPMENT .
Side 382
... operation dx d denoted by dx + a . Thus a and b being constant , we have d du bu ( de + a ) ( de + b ) u = ( a + a ) ... operation is repeated , the number of times which it is understood to be performed is expressed by an index attached ...
... operation dx d denoted by dx + a . Thus a and b being constant , we have d du bu ( de + a ) ( de + b ) u = ( a + a ) ... operation is repeated , the number of times which it is understood to be performed is expressed by an index attached ...
Side 383
... operations in the performance of which the presence of the symbol only indicates differentiation , not integration . We may with propriety term any function d d of possessing this character a direct function of dx theorem in question is ...
... operations in the performance of which the presence of the symbol only indicates differentiation , not integration . We may with propriety term any function d d of possessing this character a direct function of dx theorem in question is ...
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A Treatise on Differential Equations: Supplementary Volume George Boole Uten tilgangsbegrensning - 1865 |
Vanlige uttrykk og setninger
2ndly algebraic arbitrary constants arbitrary function assume C₁ C₂ Chap Chapter complete primitive condition Crown 8vo curve deduce derived determined differential coefficients dp dp dp dq dp dy dt dt dv du dv dv dv dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dy dz dz Edition eliminating equa exact differential expressed fcap finite given equation Hence homogeneous functions independent variable integrating factor involving method Mx+Ny obtained ordinary differential equations P₁ partial differential equation particular integral pdx+qdy primitive equation reduced relation represent respect result satisfied second member second order Shew shewn singular solution substituting suppose theorem tion transformation whence X₁ y₁