The Mathematical Writings of Duncan Farquharson Gregory |
From inside the book
Results 1-5 of 50
Page 16
... the operations indicated , Hence x2 X3 + ... ) . = = Cε- * . = 0 ( 1 - x + 1 2 - 1938 + ) - C & TM . 1.2 1.2.3 d \ -1 y = ( 1 2/2 ) * az n ax2 + Cε ̃ * • -x y = + dx Now expanding the first term 3 = ( 1- d 16 ON THE SOLUTION OF.
... the operations indicated , Hence x2 X3 + ... ) . = = Cε- * . = 0 ( 1 - x + 1 2 - 1938 + ) - C & TM . 1.2 1.2.3 d \ -1 y = ( 1 2/2 ) * az n ax2 + Cε ̃ * • -x y = + dx Now expanding the first term 3 = ( 1- d 16 ON THE SOLUTION OF.
Page 17
Duncan Farquharson Gregory, Robert Leslie Ellis William Walton. Now expanding the first term 3 = ( 1- d y = ( 1 − dx Therefore n Ꮷ + dx2- dx3 3 + ... ) ax ax2 + Cε ̃ * . n - 1 N2 y = a ... term , Y a 2n LINEAR DIFFERENTIAL EQUATIONS . 17.
Duncan Farquharson Gregory, Robert Leslie Ellis William Walton. Now expanding the first term 3 = ( 1- d y = ( 1 − dx Therefore n Ꮷ + dx2- dx3 3 + ... ) ax ax2 + Cε ̃ * . n - 1 N2 y = a ... term , Y a 2n LINEAR DIFFERENTIAL EQUATIONS . 17.
Page 18
Duncan Farquharson Gregory, Robert Leslie Ellis William Walton. or , expanding the first term , Y a 2n d dt 1 n d2 + ... terms of x , y = a 2 ( n + 1 ) x2 ) α − { √ ( 1 + æ1 ) + x } + 2 ( n − 1 ) { √ ( 1 + æo ) — æ } Get d - - + c ...
Duncan Farquharson Gregory, Robert Leslie Ellis William Walton. or , expanding the first term , Y a 2n d dt 1 n d2 + ... terms of x , y = a 2 ( n + 1 ) x2 ) α − { √ ( 1 + æ1 ) + x } + 2 ( n − 1 ) { √ ( 1 + æo ) — æ } Get d - - + c ...
Page 19
... ( 1 − a ) & c . ( ~ - a . ) y = ( 1 - a ) " x - - dx dx dx x = ε " 1 " fε ̄ " 1 " Xdx , by the theorem prefixed , since in this case n = — 1 . We should properly add a term d -1 dx -a C2 LINEAR DIFFERENTIAL EQUATIONS . 19 .
... ( 1 − a ) & c . ( ~ - a . ) y = ( 1 - a ) " x - - dx dx dx x = ε " 1 " fε ̄ " 1 " Xdx , by the theorem prefixed , since in this case n = — 1 . We should properly add a term d -1 dx -a C2 LINEAR DIFFERENTIAL EQUATIONS . 19 .
Page 20
Duncan Farquharson Gregory, Robert Leslie Ellis William Walton. We should properly add a term d -1 dx -a , 0 = ce ... terms separately by parts , we get , as before , + 1 αχ 1 X = ° * ( Ji Xd ) ε 1 a x ε 3 * ( fe TM 3 * Xdx ) a x ( α ...
Duncan Farquharson Gregory, Robert Leslie Ellis William Walton. We should properly add a term d -1 dx -a , 0 = ce ... terms separately by parts , we get , as before , + 1 αχ 1 X = ° * ( Ji Xd ) ε 1 a x ε 3 * ( fe TM 3 * Xdx ) a x ( α ...
Other editions - View all
The Mathematical Writings of Duncan Farquharson Gregory (Classic Reprint) Duncan Farquharson Gregory No preview available - 2019 |
The Mathematical Writings of Duncan Farquharson Gregory William Walton,Robert Leslie Ellis,Duncan Farquharson Gregory No preview available - 2015 |
Common terms and phrases
a₁ applied arbitrary constants arithmetical asymptotes axis becomes binomial theorem C₁ Cambridge Mathematical Journal centre coefficients commutative commutative operations conic section consider cosine cosne curve determine Differential Calculus differential equations dt² dx dx dx dy dx² dy² Edition equal expression factor Finite Differences fraction functional equation geometrical given Hence infinite integral intersection inverse operation John Herschel laws of combination linear logarithms maxima and minima method motion multiplying negative original P₁ parabola pendulum perpendicular plane of xy point of suspension principles quantity represent residue result right angles roots sides singular point solution subtraction suppose surface symbols of operation tangent Taylor's theorem term theory tion triangle u₂ values variables whence