An elementary treatise on the differential calculus, in which the method of limits is exclusively made use of, by the Rev. M. O'Brien.

X CONTENTS.
CHAPTER IX.
FAOG
Application of the Differential Calculus to the Developement of
Functions; with some preliminary remarks respecting series... 77
CHAPTER X.
Determination of the Limiting Values of Vanishing Fractions........... 99
CHAPTER XI.
Determination of the Maxima and Minima values of Functions........ 112
CHAPTER XII.
Tangents and Normals to Curves. The Curvature of Curves. The
E vo lu te............................................................................. 124
CHAPTER XIII.
Polar Formule, Differentials of Areas, Surfaces, and Volumes......... 133
CHAPTER XIV.
Asym ptotes................................................................................ 142
CHAPTER XV.
On the method of tracing the general form of a Curve from its
Equation.............................................................................. 149
CHAPTER XVI.
Singular Points of Curves................................................. 158
CHAPTER XVII.
The general theory of Contact. Intersection of consecutive Curves... 170
CHAPTER XVIII.
Lagrange's Theorem. Elimination of Constants and Functions by
Differentiation. Expansion by means of this Elimination......... 180
CHAPTER XIX.
M iscellaneous T heorem s............................................................... 189
A PPEN DIX................................. 196