A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Σελίδα v
... methods and processes of his previous course . An appen- dix to the table of contents will shew what portions of the work are regarded as sufficient for the less complete , but still not unconnected study of the subject . The principles ...
... methods and processes of his previous course . An appen- dix to the table of contents will shew what portions of the work are regarded as sufficient for the less complete , but still not unconnected study of the subject . The principles ...
Σελίδα vi
... methods and the processes which belong to an earlier stage . Thus , to take an illustration from the subject of the follow- ing work , —the solution of ordinary simultaneous differential equations properly precedes that of linear ...
... methods and the processes which belong to an earlier stage . Thus , to take an illustration from the subject of the follow- ing work , —the solution of ordinary simultaneous differential equations properly precedes that of linear ...
Σελίδα vii
... methods , as applied to differential equations , lead . Generally speaking , these methods present the solution of the proposed equation as dependent upon the performance of certain inverse operations . I have endeavoured to shew in ...
... methods , as applied to differential equations , lead . Generally speaking , these methods present the solution of the proposed equation as dependent upon the performance of certain inverse operations . I have endeavoured to shew in ...
Σελίδα viii
... methods only in the latter chapters of the work , I trust that the exposition of them which is there given will repay ... method for the solution of partial differential equations of the second order given in Chap . XV . With respect to ...
... methods only in the latter chapters of the work , I trust that the exposition of them which is there given will repay ... method for the solution of partial differential equations of the second order given in Chap . XV . With respect to ...
Σελίδα ix
... methods . The demonstrations scattered through the work are also many of them new , at least in form . In recent years much light has been thrown on certain classes of differential equations by the researches of Jacobi on the Calculus ...
... methods . The demonstrations scattered through the work are also many of them new , at least in form . In recent years much light has been thrown on certain classes of differential equations by the researches of Jacobi on the Calculus ...
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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