Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 78
Сторінка iv
... methods which are to be found in all Elementary Treatises . To this , how- ever , there is one exception : it will be seen that I have made constant use of the method known by the name of the Separation of the Symbols of Operation ...
... methods which are to be found in all Elementary Treatises . To this , how- ever , there is one exception : it will be seen that I have made constant use of the method known by the name of the Separation of the Symbols of Operation ...
Сторінка 18
... method gives it under a form which is more convenient in practice ; 1 a2 + x2 1 1 2a ( − ) 3 { x + a ( − ) 3 - Differentiating r times , d ( a ) = ( − ) ′ + 1 ̧ r ( r − 1 ) ... 2.1 2a ( ~ ) } - 1 a2 + x2 - a a 1 - 1 { { # + a ...
... method gives it under a form which is more convenient in practice ; 1 a2 + x2 1 1 2a ( − ) 3 { x + a ( − ) 3 - Differentiating r times , d ( a ) = ( − ) ′ + 1 ̧ r ( r − 1 ) ... 2.1 2a ( ~ ) } - 1 a2 + x2 - a a 1 - 1 { { # + a ...
Сторінка 20
... method employed by Lagrange may be used for the determination of the successive differentials of other functions . ( 25 ) Let u = € ¢ x3 ̧ .E If a become = ccx3 ̧ € 2cxh ̧ çch ? x + h , u becomes ( x + hys ̧ € ( x2 + 2x h + } , 2 ) = 6 ...
... method employed by Lagrange may be used for the determination of the successive differentials of other functions . ( 25 ) Let u = € ¢ x3 ̧ .E If a become = ccx3 ̧ € 2cxh ̧ çch ? x + h , u becomes ( x + hys ̧ € ( x2 + 2x h + } , 2 ) = 6 ...
Сторінка 22
... method , due to Laplace * , is to be preferred . It is easily seen on effecting two or three differentiations that the form ďu of must be dx a ‚ € ** + ɑ‚_¡ € ( r − 1 ) .x ( r − 2 ) x + ar - 2 € + & c . + a , e * ̧ ( e * + 1 ) +1 ...
... method , due to Laplace * , is to be preferred . It is easily seen on effecting two or three differentiations that the form ďu of must be dx a ‚ € ** + ɑ‚_¡ € ( r − 1 ) .x ( r − 2 ) x + ar - 2 € + & c . + a , e * ̧ ( e * + 1 ) +1 ...
Сторінка 52
... method of the separation of the symbols of operation from those of quantity , this theorem may be expressed in a very convenient form , which is useful in various parts of the Integral Calculus : viz . f ( x + h ) = { 1 + h d d h2 d2 + ...
... method of the separation of the symbols of operation from those of quantity , this theorem may be expressed in a very convenient form , which is useful in various parts of the Integral Calculus : viz . f ( x + h ) = { 1 + h d d h2 d2 + ...
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