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

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SUMMARY.

CHAP. V.
Successive Differentiations, Elimination of constant, (cc. Quantities,
and Maclaurin's and Taylor's Theorems.
ARTICLE PAGE
65. General Explanation, Notation and Successive Dlfferentiations............................................. 59
67. Derivatives of various Orders, and Elimination of constant,
exponential and transcendental functions................ 64
69. Maclaurin's Theorem, and its Applications......... 68
74. Taylor's Theorem, and its Applications.................. 83
83. Given the differential coefficients belonging to the equation
u =f(x), to find the differential coefficients belonging
to the corresponding equation x = ().............. 100
84. If u be considered a function of y at the same time that y
is considered a function of x, it is required to find the differential coefficients of u considered a function of x........ 102
87. Method of Fluxions................................... 107
91. Method of Indivisibles................................ 114
92. Method of Infinitesimals............................. 116
95. Method of Derived Functions........................... 120
98. Residual Analysis.................................... 128
CHAP. VI.
Indeterminate or Vanishing Fractions.
100. General Explanation of the subject..................... 130
103. To find the true values of functions which for particular
values of the principal variable assume the form...... 133
CHAP. VII.
Maxima and Minima of Functions of one independent Variable.
109. General Explanation of terms, &c...................... 147
110. To determine when a function of one independent variable
is a maximum or a minimum, and to investigate a criterion
for distinguishing the one from the other................ 150