A Treatise on Differential Equations, Volumen1Macmillan and Company, 1877 - 496 páginas |
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Página xiii
... 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 , 269 . 238 CHAPTER XII . ORDINARY ...
... 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 , 269 . 238 CHAPTER XII . ORDINARY ...
Página 1
... curve , it defines the rate of variation of the one , y , as referred to that of the other , x , by means of the fundamental con- ception of a limit ; it expresses that ratio by a differential coefficient dy ; and of that differential ...
... curve , it defines the rate of variation of the one , y , as referred to that of the other , x , by means of the fundamental con- ception of a limit ; it expresses that ratio by a differential coefficient dy ; and of that differential ...
Página 12
... curve , i.e. of a curve determined as to its species by the form of its equation , and as to its elements by the values of the constants in that equation , correspond only definite values of the ordinate y determining the corresponding ...
... curve , i.e. of a curve determined as to its species by the form of its equation , and as to its elements by the values of the constants in that equation , correspond only definite values of the ordinate y determining the corresponding ...
Página 20
... curve , the higher and more absolute is the property which that differential equation expresses . We reserve to a future Chapter the consideration of the genesis of partial differential equations as well as of ordinary differential ...
... curve , the higher and more absolute is the property which that differential equation expresses . We reserve to a future Chapter the consideration of the genesis of partial differential equations as well as of ordinary differential ...
Página 28
... curve the species of which as dependent upon the form of its equation would be determined by a law , but an element of which , re- presented by a constant in that equation , would be left arbi- trary , so as to permit us to draw the curve ...
... curve the species of which as dependent upon the form of its equation would be determined by a law , but an element of which , re- presented by a constant in that equation , would be left arbi- trary , so as to permit us to draw the curve ...
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Términos y frases comunes
2ndly algebraic arbitrary constant arbitrary function assume C₁ C₂ Cambridge Chap Chapter College complete primitive condition Crown 8vo curve d²u deduce derived determined differential coefficients dp dq dp dy dv dv dx dx dx dy dx dz dx² dy dy dx dy dz dz dx dz dz Edition eliminating equa exact differential expressed Extra fcap fcap finite given equation Hence homogeneous functions Illustrations independent variable infinite integrating factor involving Mdx+Ndy method Mx+Ny obtained ordinary differential equations partial differential equation particular integral primitive equation Professor Prop reduced relation represent respect result satisfied second member second order Shew shewn singular solution substituting suppose theorem tion transformation V₁ V₂ whence X₁ Y₁ аф
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