Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 18
Сторінка v
... transforming a multiple Integral from one system of independent variables to another , a problem which is of frequent occurrence , but which I have not seen solved analyti- cally in any work in which the suffix notation is em- ployed ...
... transforming a multiple Integral from one system of independent variables to another , a problem which is of frequent occurrence , but which I have not seen solved analyti- cally in any work in which the suffix notation is em- ployed ...
Сторінка 28
... transformed into those of a with respect to y by means of the formulæ , dy da d2 a dy dy2 = dx dx2 dx 3 dy dy d2 2 dy dx3 3 - dx dx dy dy dy3 5 dx dy and similarly for higher orders . The reader will find the demonstration of a general ...
... transformed into those of a with respect to y by means of the formulæ , dy da d2 a dy dy2 = dx dx2 dx 3 dy dy d2 2 dy dx3 3 - dx dx dy dy dy3 5 dx dy and similarly for higher orders . The reader will find the demonstration of a general ...
Сторінка 36
... d Ꮎ dr dr de dr de . If we had three variables x , y , ≈ to be transformed into three others p , q , r , we should have three equations of the form dx = Pdp + Qdq + Rdr , dy = 36 CHANGE OF THE INDEPENDENT VARIABLE .
... d Ꮎ dr dr de dr de . If we had three variables x , y , ≈ to be transformed into three others p , q , r , we should have three equations of the form dx = Pdp + Qdq + Rdr , dy = 36 CHANGE OF THE INDEPENDENT VARIABLE .
Сторінка 67
... transformed equation , we obtain a series for the direct th powers of the roots of the original equation . ( 11 ) If we thus transform the equation in Ex . 10 , it becomes c - by + ay2 = 0 ; and if a , ẞ be the same quantities as before ...
... transformed equation , we obtain a series for the direct th powers of the roots of the original equation . ( 11 ) If we thus transform the equation in Ex . 10 , it becomes c - by + ay2 = 0 ; and if a , ẞ be the same quantities as before ...
Сторінка 269
... transformed integral becomes m nfdxxm - 1 n = ( 37 ) If du = S % = n x = - m ( 1 + x2 ) dx m { x + ( 1 + x2 ) } } " " . ( 1 − x2 ) ( 1 + x1 ) 1 1 2 x - x2 ( 1 + x2 ) dx ( 1 − x23 ) ( 1 + x1 ) § ( 38 ) If du = = = 1 24 J we have by ...
... transformed integral becomes m nfdxxm - 1 n = ( 37 ) If du = S % = n x = - m ( 1 + x2 ) dx m { x + ( 1 + x2 ) } } " " . ( 1 − x2 ) ( 1 + x1 ) 1 1 2 x - x2 ( 1 + x2 ) dx ( 1 − x23 ) ( 1 + x1 ) § ( 38 ) If du = = = 1 24 J we have by ...
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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