A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Σελίδα ix
... problems of Geometry and Optics , to partial differential equations both of the first and second order , and , as has already been intimated , to symboli- cal methods . The demonstrations scattered through the work are also many of them ...
... problems of Geometry and Optics , to partial differential equations both of the first and second order , and , as has already been intimated , to symboli- cal methods . The demonstrations scattered through the work are also many of them ...
Σελίδα xiii
... problems , 239-244 . Trajectories , 245. Curves of Pursuit , 251. Solution of a differential equation , 254. Involutes , 256 . Inverse problem of caustics , 258-263 . Direct problem , 259 . Intrinsic equation of a curve , 263. Exercises ...
... problems , 239-244 . Trajectories , 245. Curves of Pursuit , 251. Solution of a differential equation , 254. Involutes , 256 . Inverse problem of caustics , 258-263 . Direct problem , 259 . Intrinsic equation of a curve , 263. Exercises ...
Σελίδα 67
... problem which has for its object the discovery of the integrating factors of a homo- geneous equation we must have recourse to the method of the next Chapter . EXERCISES . ― 1. Shew by the application of the theorem of Art . 1 , Chap ...
... problem which has for its object the discovery of the integrating factors of a homo- geneous equation we must have recourse to the method of the next Chapter . EXERCISES . ― 1. Shew by the application of the theorem of Art . 1 , Chap ...
Σελίδα 83
... problem which they exemplify is the following . Under what condition does the equation Mdx + Ndy = 0 admit of being made integrable by a factor of the form ( v ) where v is a known and definite function of x and y ? Let us examine the ...
... problem which they exemplify is the following . Under what condition does the equation Mdx + Ndy = 0 admit of being made integrable by a factor of the form ( v ) where v is a known and definite function of x and y ? Let us examine the ...
Σελίδα 107
... problem depends , is formed . The analysis which is subjoined may throw some light upon its real nature , and shew of what general theorem that equation constitutes an expression . PROP . Whatever may be the form of the function & ( x ) ...
... problem depends , is formed . The analysis which is subjoined may throw some light upon its real nature , and shew of what general theorem that equation constitutes an expression . PROP . Whatever may be the form of the function & ( x ) ...
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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