Introduction to Analysis in One Variable - Couverture souple

Taylor, Michael E.

 
9781470456689: Introduction to Analysis in One Variable
Couverture souple
ISBN 10 : 1470456680 ISBN 13 : 9781470456689
Editeur : American Mathematical Society, 2020

Synopsis

This is a text for students who have had a three-course calculus sequence and who are ready to explore the logical structure of analysis as the backbone of calculus. It begins with a development of the real numbers, building this system from more basic objects (natural numbers, integers, rational numbers, Cauchy sequences), and it produces basic algebraic and metric properties of the real number line as propositions, rather than axioms. The text also makes use of the complex numbers and incorporates this into the development of differential and integral calculus. For example, it develops the theory of the exponential function for both real and complex arguments, and it makes a geometrical study of the curve (expit)(expit), for real tt, leading to a self-contained development of the trigonometric functions and to a derivation of the Euler identity that is very different from what one typically sees. Further topics include metric spaces, the Stone–Weierstrass theorem, and Fourier series.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l?auteur

Michael E. Taylor, University of North Carolina, Chapel Hill, NC.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2020
Langue
anglais
ISBN 10 
1470456680
ISBN 13 
9781470456689
Reliure
Broché
Nombre de pages
247
Coordonnées du fabricant
non disponible
Personne responsable
non disponible