A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page xiv
... explicit function of one variable . 57. Maclaurin's Theorem .. 97 58. Limits of Maclaurin's Theorem . 99 59. Examples of Maclaurin's Theorem 100 60-63 . Certain trigonometrical expressions and theorems 103 64-66 . xiv ANALYTICAL TABLE.
... explicit function of one variable . 57. Maclaurin's Theorem .. 97 58. Limits of Maclaurin's Theorem . 99 59. Examples of Maclaurin's Theorem 100 60-63 . Certain trigonometrical expressions and theorems 103 64-66 . xiv ANALYTICAL TABLE.
Page xv
... expressions . 75. Different forms of the problem 76. Requisite formulæ for a function of two variables 77. Transformations in terms of a new variable SECTION 5. - Successive differentiation of functions of many independent variables ...
... expressions . 75. Different forms of the problem 76. Requisite formulæ for a function of two variables 77. Transformations in terms of a new variable SECTION 5. - Successive differentiation of functions of many independent variables ...
Page xvi
... expressions . 106. Transformation of expressions involving partial derived- functions into their equivalents in terms of other variables 107 , 108. Examples illustrative of the preceding principles .... CHAPTER IV . 180 182 CERTAIN ...
... expressions . 106. Transformation of expressions involving partial derived- functions into their equivalents in terms of other variables 107 , 108. Examples illustrative of the preceding principles .... CHAPTER IV . 180 182 CERTAIN ...
Page xix
... EXPRESSIONS . 170. Object of the Chapter is the discussion of an algebraical expression in its synthetical form 171 , 172. The continuity of algebraical expressions 173. Proof that every equation has a root ..... 174. If a is a root of ...
... EXPRESSIONS . 170. Object of the Chapter is the discussion of an algebraical expression in its synthetical form 171 , 172. The continuity of algebraical expressions 173. Proof that every equation has a root ..... 174. If a is a root of ...
Page 9
... as the expressions of arithmetical ratios . See Peacock's Algebra , 2nd edition , vol . i . pp . 54 , 155 . PRICE , VOL . I. plied or divided , the resultant is the same in 3. ] 9 ON THE ABSTRACT CHARACTER OF NUMBER . 155.
... as the expressions of arithmetical ratios . See Peacock's Algebra , 2nd edition , vol . i . pp . 54 , 155 . PRICE , VOL . I. plied or divided , the resultant is the same in 3. ] 9 ON THE ABSTRACT CHARACTER OF NUMBER . 155.
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according algebraical applicable assume becomes calculated called Chapter circle coefficients consider constant contains continuous convenient corresponding curve d³u denominator derived derived-functions determine differential divided dx dy dx² dy dx dy dy dy dz elimination equal equation equicrescent equivalent Evaluate examples expand expression F(xo+h factor finite fraction function given gives greater Hence homogeneous function increases increments independent infinite infinitesimal infinity involved less limit maximum means method negative observed original partial particular pass positive powers preceding quantity reason relation replaced represent respectively result roots sides similar Similarly substituting successive suppose symbols Theorem tion true values vanish variables variation vary whence zero
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