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CONTENTS
CHAPTER IX
DIFFERENTIALSSECTION PAGE 87. Introduction................................................................................................................................................................................................................................................................................................................................................................................................131 88. Definitions................................................................................................................................................................................................................................................................................................................................................................................................131 89. Infinitesimals................................................................................................................................................................................................................................................................................................................................................................................................132 90. Derivative of the arc in rectangular coördinates................................................................................................................................................................................................................................................................................................................................................................................................134 91. Derivative of the arc in polar coördinates................................................................................................................................................................................................................................................................................................................................................................................................135 92. Formulas for finding the differentials of functions................................................................................................................................................................................................................................................................................................................................................................................................137 93. Successive differentials................................................................................................................................................................................................................................................................................................................................................................................................139 CHAPTER X
RATES94. The derivative considered as the ratio of two rates................................................................................................................................................................................................................................................................................................................................................................................................141 CHAPTER XI
CHANGE OF VARIABLE95. Interchange of dependent and independent variables................................................................................................................................................................................................................................................................................................................................................................................................148 96. Change of the dependent variable................................................................................................................................................................................................................................................................................................................................................................................................149 97. Change of the independent variable................................................................................................................................................................................................................................................................................................................................................................................................150 98. Simultaneous change of both independent and dependent variables................................................................................................................................................................................................................................................................................................................................................................................................152 CHAPTER XII
CURVATURE. RADIUS OF CURVATURE99. Curvature................................................................................................................................................................................................................................................................................................................................................................................................155 100. Curvature of a circle................................................................................................................................................................................................................................................................................................................................................................................................155 101. Curvature at a point................................................................................................................................................................................................................................................................................................................................................................................................156 102. Formulas for curvature................................................................................................................................................................................................................................................................................................................................................................................................159 103. Radius of curvature................................................................................................................................................................................................................................................................................................................................................................................................159 104. Circle of curvature................................................................................................................................................................................................................................................................................................................................................................................................161 CHAPTER XIII
THEOREM OF MEAN VALUE. INDETERMINATE FORMS105. Rolle's Theorem................................................................................................................................................................................................................................................................................................................................................................................................164 106. The Theorem of Mean Value................................................................................................................................................................................................................................................................................................................................................................................................165 107. The Extended Theorem of Mean Value................................................................................................................................................................................................................................................................................................................................................................................................166
