A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Σελίδα 1
... limit ; it expresses that ratio by a differential dy coefficient d ; and of that differential coefficient it shews how to determine the varying magnitude or value . Or , again , con- dy dx sidering as a new variable , it seeks to ...
... limit ; it expresses that ratio by a differential dy coefficient d ; and of that differential coefficient it shews how to determine the varying magnitude or value . Or , again , con- dy dx sidering as a new variable , it seeks to ...
Σελίδα 3
... limit . When such is the case , the only adequate ex- pression of those conceptions in language is through the me- dium of differential coefficients , the only adequate expression of the truths and relations of which they are the ...
... limit . When such is the case , the only adequate ex- pression of those conceptions in language is through the me- dium of differential coefficients , the only adequate expression of the truths and relations of which they are the ...
Σελίδα 18
... limit , Art . 1 , throws much light on the nature of differential equations . As the simplest illustration let the equation of a straight line y = ax + b ..... ............ .. ( 1 ) be taken as the complete primitive , a and b being ...
... limit , Art . 1 , throws much light on the nature of differential equations . As the simplest illustration let the equation of a straight line y = ax + b ..... ............ .. ( 1 ) be taken as the complete primitive , a and b being ...
Σελίδα 26
... limit to which the ratio Ay to 0 . Ax dy y , will represent dx approaches as Ax approaches Let us then first examine the interpretation of the equation M + N1y Ay = 0 ...... Ax ( 2 ) . We have M Ay Δη N ' The second member of this ...
... limit to which the ratio Ay to 0 . Ax dy y , will represent dx approaches as Ax approaches Let us then first examine the interpretation of the equation M + N1y Ay = 0 ...... Ax ( 2 ) . We have M Ay Δη N ' The second member of this ...
Σελίδα 28
... limit , to every conceivable value of x will corre- spond a value of y , determined in subjection to a continuous law - to a law however which permits us to assign one , of the values of y arbitrarily . The analytical expression of that ...
... limit , to every conceivable value of x will corre- spond a value of y , determined in subjection to a continuous law - to a law however which permits us to assign one , of the values of y arbitrarily . The analytical expression of that ...
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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