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Elements of Mathematics : Functions of a Real Variable : Elementary Theory by Nicolas Bourbaki; [translator, Philip Spain] is a nonfiction available to read on EtoBox.

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This book is an English translation of the last French edition of Bourbaki's Fonctions d'une Variable Réelle. The first chapter is devoted to derivatives, Taylor expansions, the finite increments theorem, convex functions. In the second chapter, primitives and integrals (on arbitrary intervals) are studied, as well as their dependence with respect to parameters. Classical functions (exponential, logarithmic, circular and inverse circular) are investigated in the third chapter. The fourth chapter gives a thorough treatment of differential equations (existence and unicity properties of solutions, approximate solutions, dependence on parameters) and of systems of linear differential equations. The local study of functions (comparison relations, asymptotic expansions) is treated in chapter V, with an appendix on Hardy fields. The theory of generalized Taylor expansions and the Euler-MacLaurin formula are presented in the sixth chapter, and applied in the last one to thestudy of the Gamma function on the real line as well as on the complex plane. Although the topics of the book are mainly of an advanced undergraduate level, they are presented in the generality needed for more advanced p

Who reads Elements of Mathematics : Functions of a Real Variable : Elementary Theory?

Author

Nicolas Bourbaki; [translator, Philip Spain]

Publisher

Springer Berlin

Published

2004

Language

EN

ISBN

9783642639326

Category

nonfiction

Subjects

Mathematics, Stem