A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Σελίδα v
... questions of principle as are likely to present themselves to the reflective student in connexion with the methods and processes of his previous course . An appen- dix to the table of contents will shew what portions of the work are ...
... questions of principle as are likely to present themselves to the reflective student in connexion with the methods and processes of his previous course . An appen- dix to the table of contents will shew what portions of the work are ...
Σελίδα vii
... question arises how the defect . is to be supplied ; if redundant , the more difficult question whether the redundancy is real or apparent , and in either case how it is to be dealt with , must be considered . And here the necessity of ...
... question arises how the defect . is to be supplied ; if redundant , the more difficult question whether the redundancy is real or apparent , and in either case how it is to be dealt with , must be considered . And here the necessity of ...
Σελίδα viii
... to mention that , on questions re- lating to the theory of differential equations , my obligations are greatest to Lagrange , Jacobi , Cauchy , and , of living writers , to Professor De Morgan . For methods and vill PREFACE .
... to mention that , on questions re- lating to the theory of differential equations , my obligations are greatest to Lagrange , Jacobi , Cauchy , and , of living writers , to Professor De Morgan . For methods and vill PREFACE .
Σελίδα 1
... question we must revert to the fundamental conceptions of the Differential Calculus . The Differential Calculus contemplates quantity as subject to variation ; and variation as capable of being measured . In comparing any two variable ...
... question we must revert to the fundamental conceptions of the Differential Calculus . The Differential Calculus contemplates quantity as subject to variation ; and variation as capable of being measured . In comparing any two variable ...
Σελίδα 8
... and the primitive will lead to the differential equation in question . Thus if the complete primitive be y = = ∞ . ( 1 ) , · we have on differentiation , dy dx = C and 8 [ CH . I. GENESIS OF DIFFERENTIAL EQUATIONS .
... and the primitive will lead to the differential equation in question . Thus if the complete primitive be y = = ∞ . ( 1 ) , · we have on differentiation , dy dx = C and 8 [ CH . I. GENESIS OF DIFFERENTIAL EQUATIONS .
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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