Publisher's Synopsis
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 Mathematiques speciales," I have treated this notation from the beginning, and have presupposed only a knowledge of the formal rules for calculating derivatives.
Since mathematical analysis is essentially the science of the continuum, it would seem that every course in analysis should begin, logically, with the study of irrational numbers. I have supposed, however, that the student is already familiar with that subject. The theory of incommensurable numbers is treated in so many excellent well-known works that I have thought it useless to enter upon such a discussion. As for the other fundamental notions which lie at the basis of analysis, - such as the upper limit, the definite integral, the double Integral, etc., - I have endeavored to treat them with all desirable rigor, seeking to retain the elementary character of the work, and to avoid generalizations which would be superfluous in a book intended for purposes of instruction.
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