A Treatise on the Differential Calculus |
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Page vi
... regard to x 45 ' Illustrative examples Page 21 22 22 23 25 - 26 28 29 30 31 32 33 34 ww 35 37 CHAPTER III . Successive Differentiation . • 46 Theory of the independent variable 47 Change of the independent variable 48 Order of partial ...
... regard to x 45 ' Illustrative examples Page 21 22 22 23 25 - 26 28 29 30 31 32 33 34 ww 35 37 CHAPTER III . Successive Differentiation . • 46 Theory of the independent variable 47 Change of the independent variable 48 Order of partial ...
Page 6
... 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 differential coefficients , and to de- ( 6 ) CHAPTER II ...
... 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 differential coefficients , and to de- ( 6 ) CHAPTER II ...
Page 14
... regard du dy , du and as fractions the denominators of which are insepa- dy2 rably attached to the numerators , the ... regard to Y1 as if y , were constant , du the differential of u taken with regard to y , as if y , were constant ...
... regard du dy , du and as fractions the denominators of which are insepa- dy2 rably attached to the numerators , the ... regard to Y1 as if y , were constant , du the differential of u taken with regard to y , as if y , were constant ...
Page 15
... regard to y1 , y2 , Yз , respectively ; and dx the total differential coefficient of u with regard to x . If we adopt the suffix notation , the equation ( 1 ) may be written Du du dy du dy2 du dy + 2 = + dx dy , dx 2 dy , dx dy , dx ...
... regard to y1 , y2 , Yз , respectively ; and dx the total differential coefficient of u with regard to x . If we adopt the suffix notation , the equation ( 1 ) may be written Du du dy du dy2 du dy + 2 = + dx dy , dx 2 dy , dx dy , dx ...
Page 17
... regard to x and y taken successively as separately varying . If we replace the symbol dv in the numerators of the fractions dv dv dx ' dy by the expressive forms dv , dy , we have , transforming the equation ( 2 ) from differential ...
... regard to x and y taken successively as separately varying . If we replace the symbol dv in the numerators of the fractions dv dv dx ' dy by the expressive forms dv , dy , we have , transforming the equation ( 2 ) from differential ...
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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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