Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка 14
... Whence it appears that + a X. d d + a X = € dr ( ( ell X ) . This result , when generalized , is of great importance in the solution of Differential Equations . If the function to be differentiated be ( a + 14 SUCCESSIVE DIFFERENTIATION .
... Whence it appears that + a X. d d + a X = € dr ( ( ell X ) . This result , when generalized , is of great importance in the solution of Differential Equations . If the function to be differentiated be ( a + 14 SUCCESSIVE DIFFERENTIATION .
Сторінка 32
... . Since we have d Ꮎ = 40 , x = 2 d r du dx du dx2 = = = du do = do dx 1 du 2 do du de = + x du 2 do x d'u do 2 do dx a2 d2 u 4 d02 du + 0 a do d2 u d 02 , whence 1 du d2 u du d2 u u + 32 VARIABLE . CHANGE OF THE INDEPENDENT.
... . Since we have d Ꮎ = 40 , x = 2 d r du dx du dx2 = = = du do = do dx 1 du 2 do du de = + x du 2 do x d'u do 2 do dx a2 d2 u 4 d02 du + 0 a do d2 u d 02 , whence 1 du d2 u du d2 u u + 32 VARIABLE . CHANGE OF THE INDEPENDENT.
Сторінка 33
D. F. Gregory. whence 1 du d2 u du d2 u u + + = u + x dx dx ᏧᎾ d02 +0 = 0 . Fourier , Traité de la Chaleur , p . 376 . d2y dx ( 11 ) Transform dy + into a function where s is the independent variable , having given that ds ( da ) 2 2 ...
D. F. Gregory. whence 1 du d2 u du d2 u u + + = u + x dx dx ᏧᎾ d02 +0 = 0 . Fourier , Traité de la Chaleur , p . 376 . d2y dx ( 11 ) Transform dy + into a function where s is the independent variable , having given that ds ( da ) 2 2 ...
Сторінка 37
... 7 ° dR cos 0 sin 0 + " dr d Ꮎ dR dR · Lagrange , Mémoires de Berlin , 1773 , p . 121 . Legendre , Mémoires de l'Académie des Sciences , 1788 , p . 454 . d R d R d R whence a - У CHANGE OF THE INDEPENDENT VARIABLE . 37.
... 7 ° dR cos 0 sin 0 + " dr d Ꮎ dR dR · Lagrange , Mémoires de Berlin , 1773 , p . 121 . Legendre , Mémoires de l'Académie des Sciences , 1788 , p . 454 . d R d R d R whence a - У CHANGE OF THE INDEPENDENT VARIABLE . 37.
Сторінка 38
... Whence αφ ( 1 dr d2p do d23 ¢ x2 + y2 d2p аф ( 2 + = + dx2 dy dr 2.2 + " ) , dr Ф + dr2 and therefore This equation occurs in researches on the motion of fluids . 1 аф = 0 . r dr ( 4 ) If + аф dx2 dy ? dz Ф do = 0 , we find when 2 + y2 ...
... Whence αφ ( 1 dr d2p do d23 ¢ x2 + y2 d2p аф ( 2 + = + dx2 dy dr 2.2 + " ) , dr Ф + dr2 and therefore This equation occurs in researches on the motion of fluids . 1 аф = 0 . r dr ( 4 ) If + аф dx2 dy ? dz Ф do = 0 , we find when 2 + y2 ...
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