Cauchy’s Cours d’analyse An Annotated Translation /

• Κύριοι συγγραφείς: Bradley, Robert E. (Συγγραφέας), Sandifer, C. Edward (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York, 2009.
• Σειρά: Sources and Studies in the History of Mathematics and Physical Sciences
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; History.; History of Mathematical Sciences.; Analysis.

 This is an annotated and indexed translation (from French into English) of Augustin Louis Cauchy's 1821 classic textbook Cours d'analyse. This is the first English translation of a landmark work in mathematics, one of the most influential texts in the history of mathematics. It belongs in every mathematics library, along with Newton's Principia and Euclid's Elements. The authors' style mimics the look and feel of the second French edition. It is an essentially modern textbook style, about 75% narrative and 25% theorems, proofs, corollaries. Despite the extensive narrative, it has an essentially "Euclidean architecture" in its careful ordering of definitions and theorems. It was the first book in analysis to do this. Cauchy's book is essentially a precalculus book, with a rigorous exposition of the topics necessary to learn calculus. Hence, any good quality calculus student can understand the content of the volume. The basic audience is anyone interested in the history of mathematics, especially 19th century analysis. In addition to being an important book, the Cours d'analyse is well-written, packed with unexpected gems, and, in general, a thrill to read. Robert E. Bradley is Professor of Mathematics at Adelphi University. C. Edward Sandifer is Professor of Mathematics at Western Connecticut State University. 

 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 equations for 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.