Examples of the Processes of the Differential and Integral Calculus |
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Page v
... 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 . So long , therefore , as the old notation adapts itself to all ...
... 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 . So long , therefore , as the old notation adapts itself to all ...
Page ix
... variable IV . Elimination of Constants and Functions PAGE 1 9 28 43 V. Application of the Differential Calculus to the Development of Functions 52 22 VI . Evaluation of Functions which for certain values of the Variable become ...
... variable IV . Elimination of Constants and Functions PAGE 1 9 28 43 V. Application of the Differential Calculus to the Development of Functions 52 22 VI . Evaluation of Functions which for certain values of the Variable become ...
Page x
... Variable 249 II . Integration by Successive Reduction 271 III . Integration of Differential Functions of Two or more Variables .... 282 IV . Integration of Differential Equations .. 291 V. Integration of Differential Equations by Series ...
... Variable 249 II . Integration by Successive Reduction 271 III . Integration of Differential Functions of Two or more Variables .... 282 IV . Integration of Differential Equations .. 291 V. Integration of Differential Equations by Series ...
Page 5
... Variables . If u = 0 be an implicit function of two variables and y , then du dy dx dx du dy ( 43 ) Let ( 44 ) ( 45 ) DIFFERENTIATION . 5.
... Variables . If u = 0 be an implicit function of two variables and y , then du dy dx dx du dy ( 43 ) Let ( 44 ) ( 45 ) DIFFERENTIATION . 5.
Page 7
... Variables . ( 53 ) u = ( - ) ( 54 ) du dx = du = u = du \ x2 + y2 2xy2 du 2x2y ( x2 + y2 ) # ( x2 — y2 ) } ' - ( x2 + y2 ) } ( x2 − y3 ) } ' dy 2xy ( ydx - xdy ) ( x2 + y2 ) § ( x2 − y3 ) ś x + y§ x + y " - y - x - 2 ( xy ) - - = x ...
... Variables . ( 53 ) u = ( - ) ( 54 ) du dx = du = u = du \ x2 + y2 2xy2 du 2x2y ( x2 + y2 ) # ( x2 — y2 ) } ' - ( x2 + y2 ) } ( x2 − y3 ) } ' dy 2xy ( ydx - xdy ) ( x2 + y2 ) § ( x2 − y3 ) ś x + y§ x + y " - y - x - 2 ( xy ) - - = x ...
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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