Examples of the Processes of the Differential and Integral Calculus |
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Page i
... CAMBRIDGE : PRINTED AT THE UNIVERSITY PRESS , R PUBLISHED BY J. AND J. J. DEIGHTON ; AND SOLD BY SIMPKIN , MARSHALL & CO . , AND GEORGE BELL , LONDON . M.DCCC . XLVI . LIBRAS PREFACE . THE chief object of the present work CHAPTER PART ...
... CAMBRIDGE : PRINTED AT THE UNIVERSITY PRESS , R PUBLISHED BY J. AND J. J. DEIGHTON ; AND SOLD BY SIMPKIN , MARSHALL & CO . , AND GEORGE BELL , LONDON . M.DCCC . XLVI . LIBRAS PREFACE . THE chief object of the present work CHAPTER PART ...
Page vii
... 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.
... 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
... Progress of Analysis in the Transactions of the British Association ; and to two papers by Mr Great- heed in the Cambridge Mathematical Journal , Vol . 1 . SECT . 1. Functions of One Variable . ( 1 IL Successive Differentiation.
... Progress of Analysis in the Transactions of the British Association ; and to two papers by Mr Great- heed in the Cambridge Mathematical Journal , Vol . 1 . SECT . 1. Functions of One Variable . ( 1 IL Successive Differentiation.
Page 11
... Cambridge Transactions , Vol . v . p . 342 . u = ε du dx ax ar cos nx , = € o * ( a cos n x n sin nx ) . = tan , so that α = ( a2 + n2 ) 3 cos p , du Then = da = n = ( a2 + n2 ) 1 sin . sin o sin nx ) ( a2 + n2 ) 3 6a * ( cos & cos nx ...
... Cambridge Transactions , Vol . v . p . 342 . u = ε du dx ax ar cos nx , = € o * ( a cos n x n sin nx ) . = tan , so that α = ( a2 + n2 ) 3 cos p , du Then = da = n = ( a2 + n2 ) 1 sin . sin o sin nx ) ( a2 + n2 ) 3 6a * ( cos & cos nx ...
Page 40
... Cambridge Mathe- matical Journal , Vol . 1. p . 122 . ( 7 ) Transform the double integral 1 ffx - yn- dy dx Sam - 1 into one where u and v are the independent variables , x , y , u , v being connected by the equations x + y = u , y = UV ...
... Cambridge Mathe- matical Journal , Vol . 1. p . 122 . ( 7 ) Transform the double integral 1 ffx - yn- dy dx Sam - 1 into one where u and v are the independent variables , x , y , u , v being connected by the equations x + y = u , y = UV ...
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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