A Treatise on the Differential Calculus |
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Page vii
... Partial elimination of constants 57 Elimination of irrational , logarithmic , exponential , and circular functions ... differential coefficients 120 81 Application of indeterminate multipliers to problems of maxima and minima 122 CHAPTER ...
... Partial elimination of constants 57 Elimination of irrational , logarithmic , exponential , and circular functions ... differential coefficients 120 81 Application of indeterminate multipliers to problems of maxima and minima 122 CHAPTER ...
Page ix
... partial differential coefficients 134 Another method of finding the radius of curvature 209 ρ CHAPTER VI . Analytical Determination of the Centre of Curvature CONTENTS . ix.
... partial differential coefficients 134 Another method of finding the radius of curvature 209 ρ CHAPTER VI . Analytical Determination of the Centre of Curvature CONTENTS . ix.
Page x
... partial differential coefficients of u 211 137 Locus of the centre of curvature 212 138 The normal at any point of the involute a tangent at the corresponding point of the evolute 213 · · 140 139 Generation of the involute by the end of ...
... partial differential coefficients of u 211 137 Locus of the centre of curvature 212 138 The normal at any point of the involute a tangent at the corresponding point of the evolute 213 · · 140 139 Generation of the involute by the end of ...
Page 14
... differential coefficients as ordinary algebraical fractions : thus Du + du dy du dy , dx dy , dx dy dx = ( 2 ) , may be written , multiplying both sides of the equation by dx , Du = d ̧ ̧u + du ... • ( 3 ) . The quantity du denotes the ...
... differential coefficients as ordinary algebraical fractions : thus Du + du dy du dy , dx dy , dx dy dx = ( 2 ) , may be written , multiplying both sides of the equation by dx , Du = d ̧ ̧u + du ... • ( 3 ) . The quantity du denotes the ...
Page 15
... partial differential coefficients Du of u with regard to y1 , y2 , respectively . Finally , is called the total differential coefficient of u . dx The equation ( 3 ) shews that the total differential of u is equal to the sum of its ...
... partial differential coefficients Du of u with regard to y1 , y2 , respectively . Finally , is called the total differential coefficient of u . dx The equation ( 3 ) shews that the total differential of u is equal to the sum of its ...
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Common terms and phrases
algebraical arbitrary functions asymptote axis Cambridge change sign constant cosec curve d'u dy d²r d²u d²x d²z d2z d2z d³u d³x d³y d³z denote df df df dx DIFFERENTIAL CALCULUS differential equations du du dy du² dv₁ dx dx dx dy dx dx dz dx² dx³ dxdy dy dF dy dx dy dy dy dy dz dy₁ dy₂ dy³ dz dx dz dy dz dz eliminate expression f(y₁ find the Differential formula ƒ Y₁ Hence implicit function increment independent variables indeterminate limit maxima and minima maximum or minimum minimum value multiplying negative partial differential coefficients points of inflection positive quantity putting regard shews Suppose tangent Taylor's Theorem total differential Trinity College University of Cambridge whence y+dy Y₁ Y₂ zero бу бх
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