A Treatise on Differential Equations, Volum 1Macmillan, 1872 - 85 sider |
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Resultat 1-5 av 45
Side 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 . 209 238 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 . 209 238 CHAPTER XII . ORDINARY ...
Side 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 dy coefficient d ; 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 dy coefficient d ; and of that differential ...
Side 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 ...
Side 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 ...
Side 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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A Treatise on Differential Equations: Supplementary Volume George Boole Uten tilgangsbegrensning - 1865 |
Vanlige uttrykk og setninger
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