A Treatise on the Differential Calculus |
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Page viii
... expression for R , . 134 136 89 90 137 140 141 146 Lagrange's theory of Functions Stirling's theorem . 91 Examples of the application of Stirling's theorem 94 149 92 Extension of Taylor's theorem to functions of two variables 93 Failure ...
... expression for R , . 134 136 89 90 137 140 141 146 Lagrange's theory of Functions Stirling's theorem . 91 Examples of the application of Stirling's theorem 94 149 92 Extension of Taylor's theorem to functions of two variables 93 Failure ...
Page ix
... Expression for p when x is the independent variable 131 Expressions for p when s is the independent variable 132 Expression for p in terms of dx , dy , d'x , d'y 203 - 204 206 207 133 Expression for p in terms of partial differential ...
... Expression for p when x is the independent variable 131 Expressions for p when s is the independent variable 132 Expression for p in terms of dx , dy , d'x , d'y 203 - 204 206 207 133 Expression for p in terms of partial differential ...
Page 2
... expression whatever involving x , y , and constants . These constants are usually called parameters , a term borrowed from the theory of conic sections , where the word parameter is used to denote a certain fixed line . If we wish to ...
... expression whatever involving x , y , and constants . These constants are usually called parameters , a term borrowed from the theory of conic sections , where the word parameter is used to denote a certain fixed line . If we wish to ...
Page 6
... expression dx and dy are any quantities whatever , either finite or infinitesimal , which are in the ratio of the dy ultimate values of 8x and dy . The fraction is called the dx differential coefficient of y with regard to x , the ...
... expression dx and dy are any quantities whatever , either finite or infinitesimal , which are in the ratio of the dy ultimate values of 8x and dy . The fraction is called the dx differential coefficient of y with regard to x , the ...
Page 14
... expressions du du dy , ' dy2 , we shall then be at liberty to treat these 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 ...
... expressions du du dy , ' dy2 , we shall then be at liberty to treat these 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 ...
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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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