A Treatise on Differential Equations, Volumen1Macmillan and Company, 1877 - 496 páginas |
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Página 145
... note that the final criteria d dy dc = 0 , d.x dc = 0 are in effect analytical expressions of what logicians term con- ditional propositions . The former expresses that if x be assumed constant , y will not vary for an infinitesimal ...
... note that the final criteria d dy dc = 0 , d.x dc = 0 are in effect analytical expressions of what logicians term con- ditional propositions . The former expresses that if x be assumed constant , y will not vary for an infinitesimal ...
Página 186
... NOTE . The reader is reminded that in all references to the general con dp ditions = ∞ and dy d dx ( = ∞ , the ∞ means simply " infinity ” irrespec- tively of sign . See General Theorem , Art . 11 . " CHAPTER IX . ON DIFFERENTIAL ...
... NOTE . The reader is reminded that in all references to the general con dp ditions = ∞ and dy d dx ( = ∞ , the ∞ means simply " infinity ” irrespec- tively of sign . See General Theorem , Art . 11 . " CHAPTER IX . ON DIFFERENTIAL ...
Página 223
... note ) . Ex . Given y + 3x dy + 2y ( d ) + ( a2 + 2y3 dy ) day . dx da = 0 . Supposing the above an exact differential , we are by defi- nition permitted to write ( dy ) ' + ( x2 + 2y3 dy ) day } dx ... ( 34 ) . + 3x dy + 2y ( dy ) dU ...
... note ) . Ex . Given y + 3x dy + 2y ( d ) + ( a2 + 2y3 dy ) day . dx da = 0 . Supposing the above an exact differential , we are by defi- nition permitted to write ( dy ) ' + ( x2 + 2y3 dy ) day } dx ... ( 34 ) . + 3x dy + 2y ( dy ) dU ...
Página 232
... note by Poisson on page 239 of the edition of 1808 should be consulted ; it relates to the second of the above two propositions . See also Lacroix , Traité du Calcul Diffé- rentiel ... , Tome II . pp . 382 and 390. ] 10. We proceed to ...
... note by Poisson on page 239 of the edition of 1808 should be consulted ; it relates to the second of the above two propositions . See also Lacroix , Traité du Calcul Diffé- rentiel ... , Tome II . pp . 382 and 390. ] 10. We proceed to ...
Página 327
... Note at the end of the volume . ] Differentiating the equation u = ( v ) with respect to all the variables , we have du = q ( v ) dv , or du du dx + dx dy dy + du dz dz = & ' ( v ) ( de ex dx + and as this equation is to hold true dv dv ...
... Note at the end of the volume . ] Differentiating the equation u = ( v ) with respect to all the variables , we have du = q ( v ) dv , or du du dx + dx dy dy + du dz dz = & ' ( v ) ( de ex dx + and as this equation is to hold true dv dv ...
Otras ediciones - Ver todas
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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