Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 77
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 17
... method gives it under a form which is more convenient in practice ; 1 a2 + x 2 1 = 2a ( - ) x + a ( - ) x - a - Differentiating r times , 1 d − ( − ) ' + 1 ̧ † ( r − 1 ) ... ..2 . - { = ( ~ ) " + 1 " T 1 a2 + x2 1 2a ( - ) { { x + a ...
... method gives it under a form which is more convenient in practice ; 1 a2 + x 2 1 = 2a ( - ) x + a ( - ) x - a - Differentiating r times , 1 d − ( − ) ' + 1 ̧ † ( r − 1 ) ... ..2 . - { = ( ~ ) " + 1 " T 1 a2 + x2 1 2a ( - ) { { x + a ...
Сторінка 19
... method employed by Lagrange may be used for the determination of the successive differentials of other functions . ( 25 ) Let u = € ¤12 . If x become x + h , u becomes © ( x + h ) 2 = C ( x2 + 2x h + h2 ) = = 6 © × 2 . 62 cxh ̧ ̧ch2 Now ...
... method employed by Lagrange may be used for the determination of the successive differentials of other functions . ( 25 ) Let u = € ¤12 . If x become x + h , u becomes © ( x + h ) 2 = C ( x2 + 2x h + h2 ) = = 6 © × 2 . 62 cxh ̧ ̧ch2 Now ...
Сторінка 21
... method , due to Laplace * , is to be preferred . It is easily seen on effecting two or three differentiations that the form d'u of dx must be z a‚é TM 3 + α , -16 ( r − 1 ) = + ɑ‚_2 € ( r − 2 ) ≈ + & c . + α1e * A ‚ z ( ε * + 1 ) ' + ...
... method , due to Laplace * , is to be preferred . It is easily seen on effecting two or three differentiations that the form d'u of dx must be z a‚é TM 3 + α , -16 ( r − 1 ) = + ɑ‚_2 € ( r − 2 ) ≈ + & c . + α1e * A ‚ z ( ε * + 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 12 d dx ...
... 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 12 d dx ...
Інші видання - Показати все
Загальні терміни та фрази
a² b2 a²x² angle arbitrary constant assume asymptote becomes branches C₁ Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx 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 radius SECT singular points singular solution spiral Substituting subtangent surface tangent plane theorem triangle University of Cambridge vanish whence x²)³