A Treatise on Differential Equations, Volume 1 |
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Page ix
... equation , to integrating factors , to singular solutions , to the inverse 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 ...
... equation , to integrating factors , to singular solutions , to the inverse 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 ...
Page xii
... equations and for equations of the form F1 ( xy ) ydx + F2 ( xy ) xdy = 0 , 59—62 . Exercises , 67 . CHAPTER V. ON THE GENERAL DETERMINATION OF THE INTEGRATING FACTORS OF THE EQUATION Mdx + Ndy = 0 . Partial differential equation for ...
... equations and for equations of the form F1 ( xy ) ydx + F2 ( xy ) xdy = 0 , 59—62 . Exercises , 67 . CHAPTER V. ON THE GENERAL DETERMINATION OF THE INTEGRATING FACTORS OF THE EQUATION Mdx + Ndy = 0 . Partial differential equation for ...
Page xiv
... equations , 294. Of more than two , 298. Linear equations with constant coefficients , 300. Equations of an order higher than the first , 307. Exercises , 316 . CHAPTER XIV . OF PARTIAL DIFFERENTIAL EQUATIONS • Nature , 319. Primary ...
... equations , 294. Of more than two , 298. Linear equations with constant coefficients , 300. Equations of an order higher than the first , 307. Exercises , 316 . CHAPTER XIV . OF PARTIAL DIFFERENTIAL EQUATIONS • Nature , 319. Primary ...
Page xv
... equations , 418 . Pfaff's equation , 430. Equations not binomial , 432. Solution by series , 437. Evaluation of series , 441. Generalization , 446 . Theorem of development , 447. Laplace's reduction of partial differential equations ...
... equations , 418 . Pfaff's equation , 430. Equations not binomial , 432. Solution by series , 437. Evaluation of series , 441. Generalization , 446 . Theorem of development , 447. Laplace's reduction of partial differential equations ...
Page 3
... partial differential coefficients , and therefore in- dicating the existence of two or more independent variables with respect to which those differential coefficients have been formed . Thus an equation such as ( 2 ) or ( 3 ) ...
... partial differential coefficients , and therefore in- dicating the existence of two or more independent variables with respect to which those differential coefficients have been formed . Thus an equation such as ( 2 ) or ( 3 ) ...
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Common terms and phrases
2ndly algebraic arbitrary constant arbitrary function assume C₁ C₂ Cambridge Chap Chapter College complete primitive condition corresponding Crown 8vo curve deduce degree derived determined differential coefficients dp dy dv dv dx dx dx dy dy dx dz dx² 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 P₁ partial differential equation particular integral primitive equation Professor Prop reduced relation represent respect result satisfied second member second order Shew singular solution substituting suppose Taylor's theorem theorem tion transformation V₁ whence y₁ аф
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