Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 65
Сторінка 15
... substituting x + h for x in u " it becomes ( u + h + ch ) ; ď u ht and will be the coefficient of in the expan- dx 1. 2 . sion of this trinomial . Developing it as a binomial , of which u + u'h is the first term , we obtain ( u + b ) + ...
... substituting x + h for x in u " it becomes ( u + h + ch ) ; ď u ht and will be the coefficient of in the expan- dx 1. 2 . sion of this trinomial . Developing it as a binomial , of which u + u'h is the first term , we obtain ( u + b ) + ...
Сторінка 27
... Substituting the expansion of u in this equation , we get Σ { ( 2i - n ) Q ; x " } = 0 , or Σ { ( 2in ) Q } 0. * • This extension of a property of Laplace's Functions was communicated to me by Mr Archibald Smith . CHAPTER III . CHANGE ...
... Substituting the expansion of u in this equation , we get Σ { ( 2i - n ) Q ; x " } = 0 , or Σ { ( 2in ) Q } 0. * • This extension of a property of Laplace's Functions was communicated to me by Mr Archibald Smith . CHAPTER III . CHANGE ...
Сторінка 31
... substituting these binomial factors , we find d " u y ” = dyn [ { a - ( n - d dx - ( n - ... ( 7 ) Change the independent variable in d dx - d U. dx . - ( 1 − y2 ) d2 u dy - y dy du + n2 u = 0 The result is from y tox , having given y ...
... substituting these binomial factors , we find d " u y ” = dyn [ { a - ( n - d dx - ( n - ... ( 7 ) Change the independent variable in d dx - d U. dx . - ( 1 − y2 ) d2 u dy - y dy du + n2 u = 0 The result is from y tox , having given y ...
Сторінка 33
... dr d 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.
... dr d 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 36
... Substituting these values in the double integral it becomes SSV dx dy da dy - 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 ...
... Substituting these values in the double integral it becomes SSV dx dy da dy - 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 ...
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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