A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Σελίδα v
... possible to the historical order of their development . I presume that few who have paid any attention to the history of the Mathematical Analysis , will doubt that it has been developed in a certain order , or that that order has been ...
... possible to the historical order of their development . I presume that few who have paid any attention to the history of the Mathematical Analysis , will doubt that it has been developed in a certain order , or that that order has been ...
Σελίδα vi
... possible through the methods and the processes which belong to an earlier stage . Thus , to take an illustration from the subject of the follow- ing work , —the solution of ordinary simultaneous differential equations properly precedes ...
... possible through the methods and the processes which belong to an earlier stage . Thus , to take an illustration from the subject of the follow- ing work , —the solution of ordinary simultaneous differential equations properly precedes ...
Σελίδα xi
... possible , how many independent , 15. Cri- terion of derivation from a common primitive , 16. General form of equations thus related , 17. Geometrical illustrations , 18 . Exercises , 20 . PAGE 1 CHAPTER II . ON DIFFERENTIAL EQUATIONS ...
... possible , how many independent , 15. Cri- terion of derivation from a common primitive , 16. General form of equations thus related , 17. Geometrical illustrations , 18 . Exercises , 20 . PAGE 1 CHAPTER II . ON DIFFERENTIAL EQUATIONS ...
Σελίδα xiv
... possible , 364. Relations of first integrals , 366. General rule , 369. Miscellaneous theorems . Poisson's method , 375 . Duality , 376. Legendre's Transformation , 379. Exercises , 380 . 361 CHAPTER XVI . SYMBOLICAL METHODS Laws of ...
... possible , 364. Relations of first integrals , 366. General rule , 369. Miscellaneous theorems . Poisson's method , 375 . Duality , 376. Legendre's Transformation , 379. Exercises , 380 . 361 CHAPTER XVI . SYMBOLICAL METHODS Laws of ...
Σελίδα 6
... through the medium of differential coefficients . Now the chief object of the study of differential equations is to enable us to determine whenever it is possible , and in the most 6 [ CH . I. SPECIES , ORDER AND DEGREE .
... through the medium of differential coefficients . Now the chief object of the study of differential equations is to enable us to determine whenever it is possible , and in the most 6 [ CH . I. SPECIES , ORDER AND DEGREE .
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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