Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Результати 1-5 із 41
Сторінка i
... CAMBRIDGE : PRINTED AT THE UNIVERSITY PRESS , PUBLISHED BY J. AND J. J. DEIGHTON ; AND SOLD BY SIMPKIN , MARSHALL & CO . , AND GEORGE BELL , LONDON M. DCCC.XLVI . PREFACE . THE chief object of the present work is PART.
... CAMBRIDGE : PRINTED AT THE UNIVERSITY PRESS , PUBLISHED BY J. AND J. J. DEIGHTON ; AND SOLD BY SIMPKIN , MARSHALL & CO . , AND GEORGE BELL , LONDON M. DCCC.XLVI . PREFACE . THE chief object of the present work is PART.
Сторінка 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.
Сторінка 9
... Report on the 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 . ( 1 ) ( 2 ) d u dx SECT Successive Differentiation.
... Report on the 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 . ( 1 ) ( 2 ) d u dx SECT Successive Differentiation.
Сторінка 11
... Cambridge Transactions , Vol . v . p . 342 . ax u = ε cos nx , du dx ax = € a * ( a cos n x - n sin nx ) . = tan , so that Then α = du dx ( a2 + n2 ) 1 cos , n = ( a2 + n2 ) sin . = = ax ( a2 + n2 ) 1 a * ( cos cos nx - o · ( a2 + n2 ) ...
... Cambridge Transactions , Vol . v . p . 342 . ax u = ε cos nx , du dx ax = € a * ( a cos n x - n sin nx ) . = tan , so that Then α = du dx ( a2 + n2 ) 1 cos , n = ( a2 + n2 ) sin . = = ax ( a2 + n2 ) 1 a * ( cos cos nx - o · ( a2 + n2 ) ...
Сторінка 40
... Cambridge Mathe- matical Journal , Vol . 1. p . 122 . ( 7 ) Transform the double integral fam - 1yn - 1 dy dx 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 fam - 1yn - 1 dy dx 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 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