A Treatise on Differential Equations |
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Page 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 ...
Page xiii
... problems , 239-244 . Trajectories , 245 . 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 , 269 . CHAPTER ...
... problems , 239-244 . Trajectories , 245 . 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 , 269 . CHAPTER ...
Page 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 . II ...
... 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 . II ...
Page 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 ...
Page 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 constant arbitrary function assume C₁ C₂ Cambridge Chap Chapter cloth complete primitive condition Crown 8vo curve deduce determined differential coefficients dp dq dp dy dt dt dv dv dv dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dz Edition EDUCATIONAL BOOKS elementary eliminating equa exact differential example expressed fcap finite given equation gives Hence homogeneous functions independent variable integrating factor involving Mdx+Ndy method Mx+Ny obtained ordinary differential equations partial differential equation particular integral primitive equation problem reduced relation represent respect result satisfied second member second order shew singular solution substituting suppose theorem tion transformation TREATISE whence X₁ Y₁ аф
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