A Treatise on the Differential Calculus

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Deightons, 1846 - Differential calculus - 263 pages

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Contents

Differential coefficient of cotx 43 Differential coefficient of secx
34
Differential coefficient of cosecx 45 Differentiation of simple functions of y with regard to x
35
45 Illustrative examples Page 21 22 22 23
37
ww
38
Successive Differentiation
44
Change of the independent variable
46
Order of partial differentiations indifferent
50
Successive differentiation of an explicit function of two func tions of a single variable
52
Successive differentiation of an implicit function of a single
55
variable Successive total differentials
57
Successive differentiation of an explicit function of three vari ables one of which is a function of the other
58
Change of variables
60
46
61
5555
69
688
72
63
84
68
99
74
107
Definition of an asymptote Method of finding asymptotes
109
110111 Asymptotes of algebraic curves
110
Application of indeterminate multipliers to problems of maxima
122
CHAPTER VII
128
Transformation of one system of independent variables into another
133
Cauchys expression for R
134
Examples of Taylors theorem
136
Lagranges theory of Functions
137
Stirlings theorem
140
Examples of the application of Stirlings theorem
141
Extension of Taylors theorem to functions of two variables
146
Failure of the development of fx+h y+k by Taylors theorem
149
Limits and remainders of the development of ƒ x + h y + k 95 Example of the application of Taylors theorem for two variables
150
Stirlings theorem applied to functions of two variables
151
Lagranges formula for the development of implicit functions
152
Laplaces formula for the development of implicit functions
155
SECOND PART CHAPTER I
159

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