CONTENTS. 



I. DEFINITIONS. Limit. Infinite . 1 



t 



II. Definition of a differential coefficient. Differential coef- 



ficient of a sum, product, and quotient . . 15 



III. Differential coefficients of simple functions . . .26 

 1Y. Differential coefficients of the inverse trigonometrical 



functions and of complex functions ... 34 



V. Successive differentiation . . . . .57 



VI. Expansion of functions in series .... 68 



VII. Examples of expansion of functions . . . .87 



VIII. Successive differentiation. Differentiation of a function 



of two variables ..... 98 



IX. Lagrange's theorem and Laplace's theorem . .111 



X. Limiting values of functions which assume an indeter- 



minate form . . . . . .122 



XL Differential coefficient of a function of functions and of 



implicit functions . . . . . .148 



XII. Change of the independent variable . . . 174 



XIII. Maxima and minima values of a function of one variable . 193 



XIV. Expansion of a function of two independent variables . 219 



XV. Maxima and minima values of a function of two inde- 



pendent variables ...... 226 



XVI. Maxima and minima values of a function of several 



variables ...... 248 



XVII. Elimination of constants and functions , . . 265 



