Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 69
Сторінка 13
... expressions , it appears that d ( a ) dx ( 15 ) uv = x ^ log ∞ , ď ( uv ) da 12 ( a ) € xx " . · = n ( n − 1 ) ... ( n − r + 1 ) x ” - ” { log x + r . - r ( r− 1 ) 1.2 r ( r− 1 ) ( r− 2 ) 1 ( n − r + 1 ) ( n − r + 2 ) - 1.2 - - ( ...
... expressions , it appears that d ( a ) dx ( 15 ) uv = x ^ log ∞ , ď ( uv ) da 12 ( a ) € xx " . · = n ( n − 1 ) ... ( n − r + 1 ) x ” - ” { log x + r . - r ( r− 1 ) 1.2 r ( r− 1 ) ( r− 2 ) 1 ( n − r + 1 ) ( n − r + 2 ) - 1.2 - - ( ...
Сторінка 29
... expression for the radius of curvature when a is the independent variable is dy + dx - d2y dx2 When y is made the independent variable , it becomes da d { 1 + ( - / - ) " } d2x dy ( 3 ) Transform d2y ' dy dy 3 -x CHANGE OF THE ...
... expression for the radius of curvature when a is the independent variable is dy + dx - d2y dx2 When y is made the independent variable , it becomes da d { 1 + ( - / - ) " } d2x dy ( 3 ) Transform d2y ' dy dy 3 -x CHANGE OF THE ...
Сторінка 31
... expressing d'u and dy2 d3 u dy3 in terms of the differentials of u and y with regard to x , we may effect the required transformation more simply by differentiating successively and simplifying at each step . CHANGE OF THE INDEPENDENT ...
... expressing d'u and dy2 d3 u dy3 in terms of the differentials of u and y with regard to x , we may effect the required transformation more simply by differentiating successively and simplifying at each step . CHANGE OF THE INDEPENDENT ...
Сторінка 33
... Ꮎ dy dr cos - r sin 0 , = sin + cos 0 ; de d Ꮎ dr sin + r cos dy de and therefore = da dr cos e - r sin 0 de dy Substituting this expression for " we find da 22 { ~ 2 + ( 1/60 ) * } 3 CHANGE OF THE INDEPENDENT VARIABLE . 33.
... Ꮎ dy dr cos - r sin 0 , = sin + cos 0 ; de d Ꮎ dr sin + r cos dy de and therefore = da dr cos e - r sin 0 de dy Substituting this expression for " we find da 22 { ~ 2 + ( 1/60 ) * } 3 CHANGE OF THE INDEPENDENT VARIABLE . 33.
Сторінка 35
... expressions become more com- plicated . Such cases however seldom occur . If the independent variables enter into multiple integrals , we cannot substitute directly the values of the original diffe- rentials in terms of the new ...
... expressions become more com- plicated . Such cases however seldom occur . If the independent variables enter into multiple integrals , we cannot substitute directly the values of the original diffe- rentials in terms of the new ...
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Загальні терміни та фрази
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