Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 6-10 із 60
Сторінка 28
Duncan Farquharson Gregory William Walton. CHAPTER III . CHANGE OF THE INDEPENDENT VARIABLE . SECT . 1. Functions of One Variable . IF y = f ( x ) and therefore x = f ( y ) , the successive dif- ferential coefficients of y with respect ...
Duncan Farquharson Gregory William Walton. CHAPTER III . CHANGE OF THE INDEPENDENT VARIABLE . SECT . 1. Functions of One Variable . IF y = f ( x ) and therefore x = f ( y ) , the successive dif- ferential coefficients of y with respect ...
Сторінка 34
... SECT . 2 . Functions of Two or more Variables . Let u be a function of two variables , x and y , so that du dx u = f ( , ) ; du then to express and in terms of two new variables dy r and 0 , of which x and y are 34 CHANGE OF THE ...
... SECT . 2 . Functions of Two or more Variables . Let u be a function of two variables , x and y , so that du dx u = f ( , ) ; du then to express and in terms of two new variables dy r and 0 , of which x and y are 34 CHANGE OF THE ...
Сторінка 52
... SECT . 1. Taylor's Theorem . THIS theorem , the most important in the Differential Cal- culus , and the foundation of the other theorems for the development of Functions , was first given by Brook Taylor in his Methodus Incrementorum ...
... SECT . 1. Taylor's Theorem . THIS theorem , the most important in the Differential Cal- culus , and the foundation of the other theorems for the development of Functions , was first given by Brook Taylor in his Methodus Incrementorum ...
Сторінка 56
... SECT . 2. Maclaurin's or Stirling's Theorem . This Theorem , which is usually called Maclaurin's , but which ought to bear the name of Stirling , was first given by James Stirling in his Linea Tertii Ordinis Newtoniana , p . 32 ...
... SECT . 2. Maclaurin's or Stirling's Theorem . This Theorem , which is usually called Maclaurin's , but which ought to bear the name of Stirling , was first given by James Stirling in his Linea Tertii Ordinis Newtoniana , p . 32 ...
Сторінка 63
... SECT . 3. Theorems of Lagrange and Laplace . If y be given in an equation of the form y = x + xp ( y ) , and if u = ƒ ( y ) , ƒ and being any functions whatever , then u may be expanded in ascending powers of a by the theorem . = x2 ...
... SECT . 3. Theorems of Lagrange and Laplace . If y be given in an equation of the form y = x + xp ( y ) , and if u = ƒ ( y ) , ƒ and being any functions whatever , then u may be expanded in ascending powers of a by the theorem . = x2 ...
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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