Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 65
Сторінка 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 ...
Сторінка ix
... Application of the Differential Calculus to the Development of Functions 32 52 VI . Evaluation of Functions which for certain values of the Variable become indeterminate 79 VII . Maxima and Minima ...... 94 VIII . On the Generation of ...
... Application of the Differential Calculus to the Development of Functions 32 52 VI . Evaluation of Functions which for certain values of the Variable become indeterminate 79 VII . Maxima and Minima ...... 94 VIII . On the Generation of ...
Сторінка 51
... ' ( a x − by ) , whence and therefore 1 dx a dx 1 du a dx 1 dz + + b dy 1 du b dy + - - 1 c ; 1 du c dz = 0 . CHAPTER V. APPLICATION OF THE DIFFERENTIAL CALCULUS TO THE DEVELOPMENT 4 2 ELIMINATION OF CONSTANTS AND FUNCTIONS . 51.
... ' ( a x − by ) , whence and therefore 1 dx a dx 1 du a dx 1 dz + + b dy 1 du b dy + - - 1 c ; 1 du c dz = 0 . CHAPTER V. APPLICATION OF THE DIFFERENTIAL CALCULUS TO THE DEVELOPMENT 4 2 ELIMINATION OF CONSTANTS AND FUNCTIONS . 51.
Сторінка 52
... application of it , or remark on its importance . The following is the statement of the theorem : If u = f ( x ) and a receive an increment h , then f ( x + h ) = u + du d2 u h2 h + dx da2 1.2 ď3 u h3 + + & c . da3 1.2.3 If we avail ...
... application of it , or remark on its importance . The following is the statement of the theorem : If u = f ( x ) and a receive an increment h , then f ( x + h ) = u + du d2 u h2 h + dx da2 1.2 ď3 u h3 + + & c . da3 1.2.3 If we avail ...
Сторінка 63
... application of Maclaurin's Theorem is not of much use ; and a better means of expanding implicit functions , is to be found in the Theorems of Lagrange and Laplace , to which we now proceed . SECT . 3. Theorems of Lagrange and Laplace ...
... application of Maclaurin's Theorem is not of much use ; and a better means of expanding implicit functions , is to be found in the Theorems of Lagrange and Laplace , to which we now proceed . SECT . 3. Theorems of Lagrange and Laplace ...
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a² b2 a²x² angle arbitrary constant asymptote becomes C₁ c²x² Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy 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 plane of reference radius SECT singular solution spiral Substituting subtangent surface tangent plane theorem triangle vanish whence x²)³