A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page xiv
... FUNCTIONS . SECTION 1. - The differentiation of explicit functions of one variable . 25-29 . Rules for differentiating f ( x ) ± c , cf ( x ) , ƒ ( x ) ± Þ ( x ) ± .. , ƒ ( x ) × $ ( x ) , 30. Differentiation of a " .... 31 ...
... FUNCTIONS . SECTION 1. - The differentiation of explicit functions of one variable . 25-29 . Rules for differentiating f ( x ) ± c , cf ( x ) , ƒ ( x ) ± Þ ( x ) ± .. , ƒ ( x ) × $ ( x ) , 30. Differentiation of a " .... 31 ...
Page xvi
... explicit function 155 156 157 158 162 163 165 99. Elimination of constants from an implicit function 100. Elimination of given functions 167 169 101. Trigonometrical relations expressed by differential equations 102. Formation of ...
... explicit function 155 156 157 158 162 163 165 99. Elimination of constants from an implicit function 100. Elimination of given functions 167 169 101. Trigonometrical relations expressed by differential equations 102. Formation of ...
Page xviii
... explicit functions of one variable . 145. Method of determining such ... function .... 247 153. The absolute maximum and minimum 249 SECTION 2 ... explicit function of two independent variables . 250 155. Definition of maxima and minima ...
... explicit functions of one variable . 145. Method of determining such ... function .... 247 153. The absolute maximum and minimum 249 SECTION 2 ... explicit function of two independent variables . 250 155. Definition of maxima and minima ...
Page xxii
... explicit function is explained which well exhibits some of the peculiarities of cusps 384 251. The number of double points of a curve of the nth degree . 252. The number of cusps of a curve of the nth degree 385 387 253. The relation of ...
... explicit function is explained which well exhibits some of the peculiarities of cusps 384 251. The number of double points of a curve of the nth degree . 252. The number of cusps of a curve of the nth degree 385 387 253. The relation of ...
Page 26
... function of such variables . If one variable is involved in such an expression , it is said to be a function of one variable ; if two variables are involved , to be a function of two variables ; and so ... EXPLICIT AND IMPLICIT FUNCTIONS .
... function of such variables . If one variable is involved in such an expression , it is said to be a function of one variable ; if two variables are involved , to be a function of two variables ; and so ... EXPLICIT AND IMPLICIT FUNCTIONS .
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Common terms and phrases
according algebraical angles applicable assume axis becomes Calculus called changes sign Chapter circle coefficients consider constant continuous corresponding curve derived derived-functions determine differential dimensions direction divided drawn dx dy dy dx elimination equal equation examples expression factors finite function geometrical given gives greater Hence homogeneous function increases independent infinite infinitesimal infinity involved less limit maxima maximum means method minima minimum value negative observed origin partial particular pass plane positive powers preceding properties quantity relation replaced represent respectively result roots sides similar Similarly singular value straight line substituted successive suppose symbols tangent Theorem tion true values vanish variables variation vary whence zero