CONTENTS
xi
SECTION PAGE 108. Maxima and minima treated analytically................................................................................................................................................................................................................................................................................................................................................................................................167 109. Indeterminate forms................................................................................................................................................................................................................................................................................................................................................................................................170 110. Evaluation of a function taking on an indeterminate form................................................................................................................................................................................................................................................................................................................................................................................................170 111. Evaluation of the indeterminate form................................................................................................................................................................................................................................................................................................................................................................................................171 112. Evaluation of the indeterminate form................................................................................................................................................................................................................................................................................................................................................................................................174 113. Evaluation of the indeterminate form................................................................................................................................................................................................................................................................................................................................................................................................174 114. Evaluation of the indeterminate form................................................................................................................................................................................................................................................................................................................................................................................................175 115. Evaluation of the indeterminate forms................................................................................................................................................................................................................................................................................................................................................................................................176 CHAPTER XIV
CIRCLE OF CURVATURE. CENTER OF CURVATURE116. Circle of curvature. Center of curvature................................................................................................................................................................................................................................................................................................................................................................................................178 117. Second method for finding center of curvature................................................................................................................................................................................................................................................................................................................................................................................................180 118. Center of curvature the limiting position of the intersection of normals at neighboring points................................................................................................................................................................................................................................................................................................................................................................................................181 119. Evolutes................................................................................................................................................................................................................................................................................................................................................................................................182 120. Properties of the evolute................................................................................................................................................................................................................................................................................................................................................................................................186 121. Involutes and their mechanical construction................................................................................................................................................................................................................................................................................................................................................................................................187 CHAPTER XV
PARTIAL DIFFERENTIATION122. Continuous functions of two or more independent variables................................................................................................................................................................................................................................................................................................................................................................................................190 123. Partial derivatives................................................................................................................................................................................................................................................................................................................................................................................................191 124. Partial derivatives interpreted geometrically................................................................................................................................................................................................................................................................................................................................................................................................192 125. Total derivatives................................................................................................................................................................................................................................................................................................................................................................................................194 126. Total differentials................................................................................................................................................................................................................................................................................................................................................................................................197 127. Differentiation of implicit functions................................................................................................................................................................................................................................................................................................................................................................................................198 128. Successive partial derivatives................................................................................................................................................................................................................................................................................................................................................................................................202 129. Order of differentiation immaterial................................................................................................................................................................................................................................................................................................................................................................................................203 CHAPTER XVI
ENVELOPES130. Family of curves. Variable parameter................................................................................................................................................................................................................................................................................................................................................................................................205 131. Envelope of a family of curves depending on one parameter................................................................................................................................................................................................................................................................................................................................................................................................205 132. The evolute of a given curve considered as the envelope of its normals................................................................................................................................................................................................................................................................................................................................................................................................208 133. Two parameters connected by one equation of condition................................................................................................................................................................................................................................................................................................................................................................................................209
