Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка iv
... Symbols of Operation , although the Theory of the process is not usually given in works which are likely to be in the hands of students . I have done so because I think it a matter of some importance that the use of this method should ...
... Symbols of Operation , although the Theory of the process is not usually given in works which are likely to be in the hands of students . I have done so because I think it a matter of some importance that the use of this method should ...
Сторінка v
... symbol as d which expresses the required idea better than f But what I look on as a fatal objection to the suffix integral notation is that , like the corresponding one for differentials , it is not applicable to all cases . Of this any ...
... symbol as d which expresses the required idea better than f But what I look on as a fatal objection to the suffix integral notation is that , like the corresponding one for differentials , it is not applicable to all cases . Of this any ...
Сторінка 30
... symbol of operation alone , d " 1 d n y " = € dy dx d d d nx T = E to n factors . dx This may be put under the form d { , ( ༦-1 ) , € dx 2 ) a d dx 6 d ( n - 2 ) . -1 dv d dx Now by the theorem given in Ex . 18 , 30 CHANGE OF THE ...
... symbol of operation alone , d " 1 d n y " = € dy dx d d d nx T = E to n factors . dx This may be put under the form d { , ( ༦-1 ) , € dx 2 ) a d dx 6 d ( n - 2 ) . -1 dv d dx Now by the theorem given in Ex . 18 , 30 CHANGE OF THE ...
Сторінка 52
... 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 = € f ( x ) . + + 1.2 da h d3 1.2 ...
... 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 = € f ( x ) . + + 1.2 da h d3 1.2 ...
Сторінка 133
... symbols with proper generality so as to introduce those branches of curves which do not lie in the plane of reference , we avoid the second horn of his dilemma . ( 6 ) The Catenary . This is the curve GENERATION OF CURVES . 133.
... symbols with proper generality so as to introduce those branches of curves which do not lie in the plane of reference , we avoid the second horn of his dilemma . ( 6 ) The Catenary . This is the curve GENERATION OF CURVES . 133.
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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