A Treatise on the Differential Calculus (Google eBook)

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Deightons, 1846 - Differential calculus - 263 pages
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Contents

Differentiation of a function of a function
12
Differentiation of a function of any number of functions of a single variable
15
Differentiation of an implicit function of a single variable
17
General theory of the differentiation of implicit functions of a single variable
18
Total differentiation of a function of functions of independent variables
19
36
21
Differential coefficient of cos
33
CHAPTER III
44
Order of partial differentiations indifferent
50
Successive total differentials
57
Article Pge
67
CHAPTER V
84
Failure of the method of differentials for the evaluatiou of
92
CHAPTER VI
99
Abbreviation of operation
107
CHAPTER VII
128
Another demonstration of Taylors theorem
133
Cauchys expression for Rr
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 offx+h y+k by Taylors theorem
149
Limits and remainders of the development ofx f 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
155
SECOND PART CHAPTER T Tangency 99 Definition of a tangent and of a normal
159
Inclinations of the tangent and the normal at any point of a curve to the coordinate axes
160
Equations to the tangent and the normal at any point of a curve
162
Distance of the origin of coordinates from the tangent
164
Intercepts of the tangent
165

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