Cauchy’s Cours d’analyse An Annotated Translation

In 1821, Augustin-Louis Cauchy (1789-1857) published a textbook, the Cours d’analyse, to accompany his course in analysis at the Ecole Polytechnique. It is one of the most influential mathematics books ever written. Not only did Cauchy provide a workable definition of limits and a means to make them the basis of a rigorous theory of calculus, but he also revitalized the idea that all mathematics could be set on such rigorous foundations. Today, the quality of a work of mathematics is judged in part on the quality of its rigor, and this standard is largely due to the transformation brought about by Cauchy and the Cours d’analyse.

For this translation, the authors have also added commentary, notes, references, and an index.

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..