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formerly Fellow of Christ's College, one of H.M. Inspectors of Schools, and also by H. G. Edwards, Esq., B.A., late Scholar of Queen's College. I hope therefore that the book will not be found to contain many serious.
errors.
80 CAMBRIDGE GARDENS,
NORTH KENSINGTON, W.,
November, 1886.
JOSEPH EDWARDS.
10-12 Limits. Illustrations and Fundamental Principles,
13-17 Undetermined Forms,
18-24 Four Important Undetermined Forms,
PAGES.
1
2-5
5.9
9-11
12-15
16-17
17-24
63-67 Differentiation of a", ax, log x,
68-73 The Circular Functions,
74-81 The Inverse Trigonometrical Functions,
82
Interrogative Character of the Integral Calculus,
Series,
Method IV.-By a Differential Equation,
102
103
Enumeration of Methods, .
Method I.—Algebraical and Trigonometrical Methods, 92-94
104-111 Method II.-Taylor's and Maclaurin's Theorems,
Method III.-Differentiation or Integration of known
112
113
92
94-99
99-101
101-103
114-119 Continuity and Discontinuity,
120
121-122 Formulae of Cauchy and Schlömilch and Roche,
123-124 Application to Maclaurin's Theorem and Special
Cases of Taylor's Theorem,
125
Geometrical Illustration of Lagrange-Formula,
126-128 Failure of Taylor's and Maclaurin's Theorems,
Examples of Application of Lagrange-Formula,
Bernoulli's Numbers,
129
130
Lagrange-Formula for Remainder after n Terms of
Taylor's Series,
107-109
ARTS.
145
Differentiation of an Implicit Function,
146-150 Order of Partial Differentiations Commutative,
135
135-138
151-152 Second Differential Coefficient of an Implicit Function, 138-139
156-160 Extensions of Taylor's and Maclaurin's Theorems,
161-168 Homogeneous Functions. Euler's Theorems,
APPLICATIONS TO PLANE CURVES.
CHAPTER VII.
174-178 Geometrical Results. Cartesians and Polars,
179-181 Polar Subtangent, Subnormal, etc., .
187
182-183 Polar Equations of Tangent and Normal,
184-186 Number of Tangents and Normals from a given
point to a Curve of the nth degree,
Polar Line, Conic, Cubic, etc., .
188-190 Pedal Equation of a Curve,
191-193 Pedal Curves,
194 Tangential-Polar Equation,
195-199 Important Geometrical Results,
200 Tangential Equation,
171-172
172-174
174-175
175-177
177-181
181
181-186
208-210 To find the Oblique Asymptotes,
211-213 Number of Asymptotes to a Curve of the nth degree,
214
215
216
Asymptotes parallel to the Co-ordinate Axes,
Method of Partial Fractions for Asymptotes,
Particular Cases of the General Theorem,
217-218 Limiting Form of Curve at Infinity,
219-220 Asymptotes by Inspection,