Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
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Сторінка ix
... Independent variable IV . Elimination of Constants and Functions V. PAGE 1 9 28 43 Application of the Differential Calculus to the Development of Functions 62 52 VI . Evaluation of Functions which for certain values of the Variable ...
... Independent variable IV . Elimination of Constants and Functions V. PAGE 1 9 28 43 Application of the Differential Calculus to the Development of Functions 62 52 VI . Evaluation of Functions which for certain values of the Variable ...
Сторінка 28
... } = 0. * * This extension of a property of Laplace's Functions was communicated to me by Mr Archibald Smith . CHAPTER III . CHANGE OF THE INDEPENDENT VARIABLE . SECT 28 SUCCESSIVE DIFFERENTIATION . Change of the Independent variable.
... } = 0. * * This extension of a property of Laplace's Functions was communicated to me by Mr Archibald Smith . CHAPTER III . CHANGE OF THE INDEPENDENT VARIABLE . SECT 28 SUCCESSIVE DIFFERENTIATION . Change of the Independent variable.
Сторінка 29
Duncan Farquharson Gregory. CHAPTER III . CHANGE OF THE INDEPENDENT VARIABLE . SECT . I. Functions of One Variable . IF y = f ( x ) and therefore af ( y ) , the successive dif- ferential coefficients of y with respect to a are ...
Duncan Farquharson Gregory. CHAPTER III . CHANGE OF THE INDEPENDENT VARIABLE . SECT . I. Functions of One Variable . IF y = f ( x ) and therefore af ( y ) , the successive dif- ferential coefficients of y with respect to a are ...
Сторінка 30
... curvature when a is the independent variable is + ( dy ) " } - dx A g dx2 When y is made the independent variable , it becomes ( dx 2 ) } 1 + dy dx dy ( 3 ) Transform day dx2 3 dy 3 dy 330 CHANGE OF THE INDEPENDENT VARIABLE .
... curvature when a is the independent variable is + ( dy ) " } - dx A g dx2 When y is made the independent variable , it becomes ( dx 2 ) } 1 + dy dx dy ( 3 ) Transform day dx2 3 dy 3 dy 330 CHANGE OF THE INDEPENDENT VARIABLE .
Сторінка 31
... independent variable . The result is ď2 x + x − € 3 0 . dy2 ( 4 ) Change the variable in du dy + и ( 1+ y2 ) } a from y to w , when a = log { y + ( 1 + y2 ) } } . du a The result is + u = ( ε * + € ̃ * ) . dx 2 ( 5 ) Change the variable ...
... independent variable . The result is ď2 x + x − € 3 0 . dy2 ( 4 ) Change the variable in du dy + и ( 1+ y2 ) } a from y to w , when a = log { y + ( 1 + y2 ) } } . du a The result is + u = ( ε * + € ̃ * ) . dx 2 ( 5 ) Change the variable ...
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a² b2 a²x² angle arbitrary constant asymptote axis becomes C₁ c²x² Cambridge circle co-ordinates condition curvature curve cycloid cylinder determine differential coefficients differential equation dx dx dx dy dx dx² dy dx dy dy dy dy dz eliminate ellipse equal Euler find the value formula function Geometry gives Hence hypocycloid infinite Integrating with respect intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral maximum minimum Multiply negative origin parabola perpendicular radius radius of curvature singular solution spiral Substituting subtangent surface tangent plane theorem tractory triangle vanish whence x²)³