Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Сторінка 15
... ) ( rs ) cu2 1.2 ( nr + 1 ) ( n − r + 2 ) u'1 * r ( r - 1 ) cu 1. ( n − r + 1 ) u ' * + & c . } ( A ) * Mémoires de Berlin , 1772 , p . 213 . By developing in a different manner a more convenient formula SUCCESSIVE DIFFERENTIATION . 15.
... ) ( rs ) cu2 1.2 ( nr + 1 ) ( n − r + 2 ) u'1 * r ( r - 1 ) cu 1. ( n − r + 1 ) u ' * + & c . } ( A ) * Mémoires de Berlin , 1772 , p . 213 . By developing in a different manner a more convenient formula SUCCESSIVE DIFFERENTIATION . 15.
Сторінка 21
... + 1 ) 2 + 1 1 ' } e ( r − 2 ) * + & c . ] ( r + 1 ) ~ 1 ' } e ( r − 2 ) • + & c . ] 1.2 ( +1 ) +1 * Mémoires de l'Académie , 1777 , p . 108 . SECT . 2 . Functions of Two or more Variables SUCCESSIVE DIFFERENTIATION . 21.
... + 1 ) 2 + 1 1 ' } e ( r − 2 ) * + & c . ] ( r + 1 ) ~ 1 ' } e ( r − 2 ) • + & c . ] 1.2 ( +1 ) +1 * Mémoires de l'Académie , 1777 , p . 108 . SECT . 2 . Functions of Two or more Variables SUCCESSIVE DIFFERENTIATION . 21.
Сторінка 37
... Mémoires de Berlin , 1773 , p . 121 . Legendre , Mémoires de l'Académie des Sciences , 1788 , p . 454 . dR d R dR whence x - Y dy dx CHANGE OF THE INDEPENDENT VARIABLE . 37.
... Mémoires de Berlin , 1773 , p . 121 . Legendre , Mémoires de l'Académie des Sciences , 1788 , p . 454 . dR d R dR whence x - Y dy dx CHANGE OF THE INDEPENDENT VARIABLE . 37.
Сторінка 63
... Mémoires de Berlin , 1768 , p . 251 . The Theorem of Laplace is an extension of the preceding , made by assuming the given equation in y to be d y = F { x + x + ( y ) } . Then if u = f ( y ) , and if we put ƒ F ( x ) = ƒ1 ( * ) , and ...
... Mémoires de Berlin , 1768 , p . 251 . The Theorem of Laplace is an extension of the preceding , made by assuming the given equation in y to be d y = F { x + x + ( y ) } . Then if u = f ( y ) , and if we put ƒ F ( x ) = ƒ1 ( * ) , and ...
Сторінка 75
... take the form 0 0 · An artifice of Laplace however enables us to avoid this difficulty . Since 1 x x X x x 1 2 € 1 € + 1 Mémoires de l'Académie , 1777 , p . 106 . the coefficient of " in in 啸 +1 20 x DEVELOPMENT OF FUNCTIONS . 75.
... take the form 0 0 · An artifice of Laplace however enables us to avoid this difficulty . Since 1 x x X x x 1 2 € 1 € + 1 Mémoires de l'Académie , 1777 , p . 106 . the coefficient of " in in 啸 +1 20 x DEVELOPMENT OF FUNCTIONS . 75.
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a² b2 a²x² angle arbitrary constant asymptote becomes C₁ c²x² Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy dx dy dx dx² dy dx dy dy dy dy dz dz dz eliminate ellipse equal Euler factor formula fraction function Geometry gives Hence hypocycloid infinite intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral Multiply negative origin parabola perpendicular plane of reference radius SECT singular solution spiral Substituting subtangent surface tangent plane theorem triangle vanish whence x²)³