Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 66
Сторінка 15
... substituting x + h for x in u " it becomes ( u + h + chủ ) ; ď u and will be the coefficient of h 1.2 ... in the expan- dx * 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 + chủ ) ; ď u and will be the coefficient of h 1.2 ... in the expan- dx * 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 " } - i = 0 , or Σ { ( 2i – n ) Q ; } = 0 . • This extension of a property of Laplace's Functions was communicated to me by Mr Archibald Smith . CHAPTER III ...
... Substituting the expansion of u in this equation , we get Σ { ( 2i − n ) Q ; x " } - i = 0 , or Σ { ( 2i – n ) Q ; } = 0 . • This extension of a property of Laplace's Functions was communicated to me by Mr Archibald Smith . CHAPTER III ...
Сторінка 31
... substituting these binomial factors , we find جرح d " u dy d d - [ { d - ( n - 1 ) } { / d / - ( n − 2 ) ... ( ́ - · ) 4 ] · = dx - ( 7 ) Change the independent variable in Ꮖ . и . d2 u du - ( 1 − y2 ) -y + n2 u = 0 dy2 dy from y to ...
... substituting these binomial factors , we find جرح d " u dy d d - [ { d - ( n - 1 ) } { / d / - ( n − 2 ) ... ( ́ - · ) 4 ] · = dx - ( 7 ) Change the independent variable in Ꮖ . и . d2 u du - ( 1 − y2 ) -y + n2 u = 0 dy2 dy from y to ...
Сторінка 33
... d Ꮎ = dr cos d Ꮎ - sin 0 , dy dr = de ᏧᎾ sin ✪ + r cos 0 ; dr sin + cos dy ᏧᎾ and therefore da dr cos Ꮎ - r sin o de Substituting this expression for dy 9 we find dx + { + } ( dy 23 ( 13 ) 3 CHANGE OF THE INDEPENDENT VARIABLE . 33.
... d Ꮎ = dr cos d Ꮎ - sin 0 , dy dr = de ᏧᎾ sin ✪ + r cos 0 ; dr sin + cos dy ᏧᎾ and therefore da dr cos Ꮎ - r sin o de Substituting this expression for dy 9 we find dx + { + } ( dy 23 ( 13 ) 3 CHANGE OF THE INDEPENDENT VARIABLE . 33.
Сторінка 36
... Substituting these values in the double integral it becomes SS V ( dx dy dx dy - do dr dr de dr de . If we had three variables x , y , z 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 SS V ( dx dy dx dy - do dr dr de dr de . If we had three variables x , y , z to be transformed into three others p , q , r , we should have three equations of the form dx = Pdp ...
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