A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Results 6-10 of 92
Page xiii
... symbols .. 9. Fundamental theorems on infinities and infinitesimals 10. Examples on the above theorems .. 11. The relation of the finite to the infinite and the infinitesimal 12. Functions ; on dependent and independent variables 13-15 ...
... symbols .. 9. Fundamental theorems on infinities and infinitesimals 10. Examples on the above theorems .. 11. The relation of the finite to the infinite and the infinitesimal 12. Functions ; on dependent and independent variables 13-15 ...
Page xiv
... symbols . Examples . 89 55. Leibnitz's Theorem for successive differentiation 94 56. The nth differential of ƒ ( x ) , in terms of successive values of f ( x ) 97 SECTION 2. - Expansion of an explicit function of one variable . 57 ...
... symbols . Examples . 89 55. Leibnitz's Theorem for successive differentiation 94 56. The nth differential of ƒ ( x ) , in terms of successive values of f ( x ) 97 SECTION 2. - Expansion of an explicit function of one variable . 57 ...
Page xv
... symbols ..... 128 79. The order of successive differentiations with respect to many variables is indifferent . . . . . 131 80 , 81. Application of the principles of the preceding Articles to functions of two and more variables 133 82 ...
... symbols ..... 128 79. The order of successive differentiations with respect to many variables is indifferent . . . . . 131 80 , 81. Application of the principles of the preceding Articles to functions of two and more variables 133 82 ...
Page xx
... symbols of direction . 188. Necessity of symbols of direction 189. Interpretation of + " and of + 190. Interpretation of ( - ) or of + # 191. Other modes of indicating direction 303 305 307 307 308 192. Examples in illustration of the ...
... symbols of direction . 188. Necessity of symbols of direction 189. Interpretation of + " and of + 190. Interpretation of ( - ) or of + # 191. Other modes of indicating direction 303 305 307 307 308 192. Examples in illustration of the ...
Page xxviii
... symbols of operation and symbols of quantities 419. The laws of commutation , distribution , and iteration 600 601 420. The extension of the same to algebraical functions 603 421. The law of total differentiation 604 422. Three ...
... symbols of operation and symbols of quantities 419. The laws of commutation , distribution , and iteration 600 601 420. The extension of the same to algebraical functions 603 421. The law of total differentiation 604 422. Three ...
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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