Examples of the Processes of the Differential and Integral Calculus |
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Page iv
... application readily understood . I have adhered throughout to the notation of Leib- nitz in preference to that which has been of late re- vived and partially adopted in this University . Of the Differential notation I need say nothing ...
... application readily understood . I have adhered throughout to the notation of Leib- nitz in preference to that which has been of late re- vived and partially adopted in this University . Of the Differential notation I need say nothing ...
Page ix
... 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 . Maxima and Minima . .................. . 393 94 VIII . On ...
... 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 . Maxima and Minima . .................. . 393 94 VIII . On ...
Page 25
... regard- ing homogeneous functions of any number of variables , which from the frequent applications made of it ought to be noticed in this place . If u be a homogeneous algebraic function of n dimensions SUCCESSIVE DIFFERENTIATION . 25.
... regard- ing homogeneous functions of any number of variables , which from the frequent applications made of it ought to be noticed in this place . If u be a homogeneous algebraic function of n dimensions SUCCESSIVE DIFFERENTIATION . 25.
Page 26
... applying this theorem to transcendental functions of algebraical functions , it is to be observed that it is not suffi- cient that these last should be homogeneous , it is also necessary that they should be of zero dimensions , as ...
... applying this theorem to transcendental functions of algebraical functions , it is to be observed that it is not suffi- cient that these last should be homogeneous , it is also necessary that they should be of zero dimensions , as ...
Page 51
... by ) , = - b dy 1 du whence 1 dx a dx 1 dz + 1 du and therefore + a dx b dy 1 с 1 du + = 0 . c dz CHAPTER V. APPLICATION OF THE DIFFERENTIAL CALCULUS TO THE DEVELOPMENT 4-2 ELIMINATION OF CONSTANTS AND FUNCTIONS . 51 V.
... by ) , = - b dy 1 du whence 1 dx a dx 1 dz + 1 du and therefore + a dx b dy 1 с 1 du + = 0 . c dz CHAPTER V. APPLICATION OF THE DIFFERENTIAL CALCULUS TO THE DEVELOPMENT 4-2 ELIMINATION OF CONSTANTS AND FUNCTIONS . 51 V.
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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