Examples of the Processes of the Differential and Integral Calculus |
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Page v
... differentials , it is not applicable to all cases . Of this any one may satisfy himself by attempting to use it in transforming a multiple Integral from one system of independent variables to another , a problem which is of frequent ...
... differentials , it is not applicable to all cases . Of this any one may satisfy himself by attempting to use it in transforming a multiple Integral from one system of independent variables to another , a problem which is of frequent ...
Page vii
... alterations in this department of the work , the Editor is indebted to the kindness of Mr Ellis , Fellow of Trinity College . WILLIAM WALTON . CAMBRIDGE , June , 1846 . CONTENTS . CHAPTER PART I. DIFFERENTIAL CALCULUS . I. Differentiation.
... alterations in this department of the work , the Editor is indebted to the kindness of Mr Ellis , Fellow of Trinity College . WILLIAM WALTON . CAMBRIDGE , June , 1846 . CONTENTS . CHAPTER PART I. DIFFERENTIAL CALCULUS . I. Differentiation.
Page 9
... differentials , when expressed by the notation of Leibnitz , was observed soon after the invention of the Calculus . Leibnitz himself paid much attention to this subject , as may be seen in his correspondence with John Bernoulli ; and ...
... differentials , when expressed by the notation of Leibnitz , was observed soon after the invention of the Calculus . Leibnitz himself paid much attention to this subject , as may be seen in his correspondence with John Bernoulli ; and ...
Page 19
... differentials of other functions . ( 25 ) Let u = € ¤12 . If x become x + h , u becomes © ( x + h ) 2 = C ( x2 + 2x h + h2 ) = = 6 © × 2 . 62 cxh ̧ ̧ch2 Now sh ( 2 cx ) 2 ( 2cx ) 3 = 1 + 2cx h + h2 + h3 + & c . 1.2 1.2.3 c2 C3 h1 + ho + ...
... differentials of other functions . ( 25 ) Let u = € ¤12 . If x become x + h , u becomes © ( x + h ) 2 = C ( x2 + 2x h + h2 ) = = 6 © × 2 . 62 cxh ̧ ̧ch2 Now sh ( 2 cx ) 2 ( 2cx ) 3 = 1 + 2cx h + h2 + h3 + & c . 1.2 1.2.3 c2 C3 h1 + ho + ...
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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