A Course of Mathematical Analysis, Volume I

Excerpt from A Course in Mathematical Analysis, Vol. 1: Derivatives and Differentials; Definite Integrals; Expansion in Series; Applications to Geometry
This book contains, with slight variations, the material given in my course at the University of Paris. I have modified somewhat the order followed in the lectures for the sake of uniting in a single volume all that has to do with functions of real variables, except the theory of differential equations. The differential notation not being treated in the Classe de Mathématiques spéciales, I have treated this notation from the beginning, and have presupposed only a knowledge of the formal rules for calculating derivatives.
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