A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page xv
... functions of two and more variables 133 82. Euler's Theorems of homogeneous functions 83. Transformation of partial derived functions .. 137 139 SECTION 6. - Successive differentiation of implicit functions . 84. Calculation of derived - ...
... functions of two and more variables 133 82. Euler's Theorems of homogeneous functions 83. Transformation of partial derived functions .. 137 139 SECTION 6. - Successive differentiation of implicit functions . 84. Calculation of derived - ...
Page xvi
... functions of many series .. 96. Extension to implicit functions SECTION 7. - The formation of differential equations ... partial differential expressions . 106. Transformation of expressions involving partial derived- functions into ...
... functions of many series .. 96. Extension to implicit functions SECTION 7. - The formation of differential equations ... partial differential expressions . 106. Transformation of expressions involving partial derived- functions into ...
Page 72
... partial changes or increments of the rectangle are y da and x dy . But suppose both sides to have received ... derived functions , the brackets in- dicating that they do so , and the variable in the denominator of the fractions being that , ...
... partial changes or increments of the rectangle are y da and x dy . But suppose both sides to have received ... derived functions , the brackets in- dicating that they do so , and the variable in the denominator of the fractions being that , ...
Page 73
... partial derived functions or differential coefficients . Thus much as to the symbols , their nomenclature , and their meanings . Let us now consider the most simple case of a func- tion of two independent variables . 47. ] Differentiation ...
... partial derived functions or differential coefficients . Thus much as to the symbols , their nomenclature , and their meanings . Let us now consider the most simple case of a func- tion of two independent variables . 47. ] Differentiation ...
Page 77
... partial dif- ferentials of u ; and therefore Du = DF = d ̧u + d „ u + d2u + ... ; ( 45 ) that is , the total differential is equal to the sum of the partial differentials . And if the result is expressed in terms of partial derived functions ...
... partial dif- ferentials of u ; and therefore Du = DF = d ̧u + d „ u + d2u + ... ; ( 45 ) that is , the total differential is equal to the sum of the partial differentials . And if the result is expressed in terms of partial derived functions ...
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Common terms and phrases
a₁ algebraical angles b₁ becomes Calculus change of sign changes sign circle coefficients constant cosec curve d2F d2F d²u d²x d²y d³u d³y derived function determine differential equation dr dr dr dy dx dx dx dy dx² dy dx dy dy dy dz dy² dz dx equal equicrescent explicit function expression F(xo F(xo+h factor finite quantity fraction func given Hence homogeneous function increases increments indeterminate form infinite infinitesimal Infinitesimal Calculus infinity involved logarithms loge Maclaurin's maxima and minima maximum or minimum minimum value negative partial derived-functions positive primitive equation radius replaced result right-hand member roots Similarly sin x singular value Sturm's Theorem substituting suppose symbols Theorem tion vanish variables variation versin whence zero