Examples of the Processes of the Differential and Integral Calculus |
From inside the book
Results 1-5 of 77
Page ix
... 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 indeterminate 79 VII ...
... 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 indeterminate 79 VII ...
Page 35
... Eliminating we find dy du dx = du dy · dr de Ꮎ da dy - du dy • de dr dy dx dr de dr de du Eliminating we find dx du dx du dx du dr de de dr dy dx dy dy dx - · • dr de dr de If r and be given explicitly in terms of x and y , we have at ...
... Eliminating we find dy du dx = du dy · dr de Ꮎ da dy - du dy • de dr dy dx dr de dr de du Eliminating we find dx du dx du dx du dr de de dr dy dx dy dy dx - · • dr de dr de If r and be given explicitly in terms of x and y , we have at ...
Page 36
... Eliminating de between these we find dx dx dy dy de dy dr . = do do dr dr d Ꮎ From this it follows that when dy = 0 , dr = 0. Hence we have dx - dx d Ꮎ . de Substituting these values in the double integral it becomes SS V ( dx dy dx ...
... Eliminating de between these we find dx dx dy dy de dy dr . = do do dr dr d Ꮎ From this it follows that when dy = 0 , dr = 0. Hence we have dx - dx d Ꮎ . de Substituting these values in the double integral it becomes SS V ( dx dy dx ...
Page 37
... eliminating two of the three quantities dp , dq , dr . Supposing we eliminate the last two we have da Mdp , M being a function of p , q , r . From this it follows that when da = 0 , dp = 0. Hence supposing y to vary while a and are ...
... eliminating two of the three quantities dp , dq , dr . Supposing we eliminate the last two we have da Mdp , M being a function of p , q , r . From this it follows that when da = 0 , dp = 0. Hence supposing y to vary while a and are ...
Page 42
... dx + dy ( d ) " } = ffd0d & sin 0 { a2b2 ( cos 0 ) 2 + ( c sin ( ) 2 ( a2 sin2 + b2 cos ̊p ) } 1 . Ivory , Phil . Trans . 1809 . CHAPTER IV . ELIMINATION OF CONSTANTS AND FUNCTIONS BY MEANS 42 CHANGE OF THE INDEPENDENT VARIABLE .
... dx + dy ( d ) " } = ffd0d & sin 0 { a2b2 ( cos 0 ) 2 + ( c sin ( ) 2 ( a2 sin2 + b2 cos ̊p ) } 1 . Ivory , Phil . Trans . 1809 . CHAPTER IV . ELIMINATION OF CONSTANTS AND FUNCTIONS BY MEANS 42 CHANGE OF THE INDEPENDENT VARIABLE .
Other editions - View all
Common terms and phrases
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