Cauchy’s Cours d’analyse

On real functions..- On infinitely small and infinitely large quantities, and on the continuity of functions. Singular values of functions in various particular cases..- On symmetric functions and alternating functions. The use of these functions for the solution of equations of the first degree in any number of unknowns. On homogeneous functions..- Determination of integer functions, when a certain number of particular values are known. Applications..- Determination of continuous functions of a single variable that satisfy certain conditions..- On convergent and divergent series. Rules for the convergence of series. The summation of several convergent series..- On imaginary expressions and their moduli..- On imaginary functions and variables..- On convergent and divergent imaginary series. Summation of some convergent imaginary series. Notations used to represent imaginary functions that we find by evaluating the sum of such series..- On real or imaginary roots of algebraic equationsfor which the left-hand side is a rational and integer function of one variable. The solution of equations of this kind by algebra or trigonometry..- Decomposition of rational fractions..- On recurrent series..