A Treatise on the Differential Calculus |
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Page 2
... 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 represent in the most general manner that y is an explicit function of x , we may ...
... 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 represent in the most general manner that y is an explicit function of x , we may ...
Page 6
... called the dx differential coefficient of y with regard to x , the quantities dx and dy being called the differentials of x and y . The object of the Differential Calculus is to investigate the pro- perties of differentials and ...
... called the dx differential coefficient of y with regard to x , the quantities dx and dy being called the differentials of x and y . The object of the Differential Calculus is to investigate the pro- perties of differentials and ...
Page 14
... called the partial differentials of u with regard to y1 , y2 , respectively , and Du its total differential . The quantities dv , u " dy , dyu dy2 " in the equation ( 2 ) , or their equivalents 14 PRINCIPLES OF DIFFERENTIATION .
... called the partial differentials of u with regard to y1 , y2 , respectively , and Du its total differential . The quantities dv , u " dy , dyu dy2 " in the equation ( 2 ) , or their equivalents 14 PRINCIPLES OF DIFFERENTIATION .
Page 15
... called the partial differential coefficients Du dx of u with regard to y ,, y2 , respectively . Finally , is called the total differential coefficient of u . The equation ( 3 ) shews that the total differential of u is equal to the sum ...
... called the partial differential coefficients Du dx of u with regard to y ,, y2 , respectively . Finally , is called the total differential coefficient of u . The equation ( 3 ) shews that the total differential of u is equal to the sum ...
Page 20
... called the differentials of the corresponding incre- mented quantities : this definition of differentials is merely an extension of the definition for the case of one independent variable to that of any number . Then , by the notation ...
... called the differentials of the corresponding incre- mented quantities : this definition of differentials is merely an extension of the definition for the case of one independent variable to that of any number . Then , by the notation ...
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Common terms and phrases
algebraical arbitrary functions asymptote axis Cambridge change sign College constant cosec curve d'u d'u d'u dz d²r d²u d²x d²z d2z d2z D³u d³x d³y d³z denoting df df df dx differential equations dr dr du dy du² dv₁ dx dx dx dy dx dx dz dx² dx³ dxdy dy df dy dx dy dy,dy dy² dy³ dz dx dz dy dz dz dz² eliminate expression f(y₁ find the Differential formula ƒ Y₁ Hence implicit function indefinitely independent variables indeterminate limit maxima and minima maximum or minimum minimum value negative partial differential coefficients points of inflection positive quantity proposed equation putting regard shews Suppose tangent Taylor's Theorem theorem total differential Trinity College whence y+dy Y₂ zero аф бу бх
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