A Treatise on Differential Equations, Volum 1Macmillan, 1872 - 85 sider |
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Resultat 1-5 av 73
Side xii
... Theorem of development , tion by continued fractions , 96 , 97 . linear , 103. Euler's equation , 104 . 107. Exercises , 110 . CHAPTER VII . ON DIFFERENTIAL EQUATIONS OF THE FIRST ORDER , BUT NOT OF THE FIRST DEGREE Typical form , 113 ...
... Theorem of development , tion by continued fractions , 96 , 97 . linear , 103. Euler's equation , 104 . 107. Exercises , 110 . CHAPTER VII . ON DIFFERENTIAL EQUATIONS OF THE FIRST ORDER , BUT NOT OF THE FIRST DEGREE Typical form , 113 ...
Side xiii
... theorem , 148. Geometrical interpretation , 152. Deri- vation of the singular solution from the differential equation , 153 . More general definition of singular solution , 163. Distinction of species , ib . General theorem , 164 ...
... theorem , 148. Geometrical interpretation , 152. Deri- vation of the singular solution from the differential equation , 153 . More general definition of singular solution , 163. Distinction of species , ib . General theorem , 164 ...
Side xiv
... 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 direct expressions , xiv CONTENTS .
... 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 direct expressions , xiv CONTENTS .
Side xv
... Theorem of development , 447. Laplace's reduction of partial differential equations , 450. Miscellaneous notices ... theorem , 477. Solution by Fourier's theorem , 478. Miscellaneous exercises , 481 . The following portions of the work ...
... Theorem of development , 447. Laplace's reduction of partial differential equations , 450. Miscellaneous notices ... theorem , 477. Solution by Fourier's theorem , 478. Miscellaneous exercises , 481 . The following portions of the work ...
Side 15
... theorems , viz .: 1.2 r 1st . To a given primitive involving x , y , and n arbitrary n ( n − 1 ) ( n − 2 ) ... .. ( n − r + 1 ) constants belong differential equations of the rth order ( r being any whole number less than n ) , each ...
... theorems , viz .: 1.2 r 1st . To a given primitive involving x , y , and n arbitrary n ( n − 1 ) ( n − 2 ) ... .. ( n − r + 1 ) constants belong differential equations of the rth order ( r being any whole number less than n ) , each ...
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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