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 40 f ( x ) f ( x ) ± c , cƒ ( x ) , ƒ ( x ) ± $ ( x ) ± . . , ƒ ( x ) × $ ( x ) , ( x ) 30. Differentiation of a ...
... FUNCTIONS . SECTION 1. - The differentiation of explicit functions of one variable . 25-29 . Rules for differentiating 40 f ( x ) f ( x ) ± c , cƒ ( x ) , ƒ ( x ) ± $ ( x ) ± . . , ƒ ( x ) × $ ( x ) , ( x ) 30. Differentiation of a ...
Page xvi
... explicit function 99. Elimination of constants from an implicit function 100. Elimination of given functions 165 ...... 167 169 171 172 174 101. Trigonometrical relations expressed by differential equations 102. Formation of ...
... explicit function 99. Elimination of constants from an implicit function 100. Elimination of given functions 165 ...... 167 169 171 172 174 101. 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 . 155. Definition of maxima and minima of ...
... 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 . 155. Definition of maxima and minima of ...
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 253. The relation of a ...
... 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 253. The relation of a ...
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
a₁ algebraical angles asymptote axis b₁ becomes Calculus change of sign changes sign circle coefficients constants critical values curve cycloid d2F d2F d²x d²y d2y dx2 d³u d³y determine differential equation dimensions dr dr dr dy drawn dx dx dx dy dx² dy dx dy dy dy dz dy² elimination epitrochoid equa equal equicrescent expression F(xo F(xo+h factors finite quantity function geometrical Hence homogeneous function hyperbola increases infinite infinitesimal Infinitesimal Calculus infinity maxima and minima maximum or minimum minimum value negative nth degree origin partial derived-functions pass plane of reference positive radius real roots right-hand member roots of f(x shewn Similarly singular value straight line Sturm's Theorem substituting symbols tangent Theorem tion u₁ vanish variables variations whence zero