An Interactive Introduction to Mathematical Analysis

Jonathan Lewin

524 pages, parution le 25/02/2003

Ajouter à une liste

Indisponible

Résumé

This book provides a rigorous course in the calculus of functions of a real variable. Its gentle approach, particularly in its early chapters, makes it especially suitable for students who are not headed for graduate school but, for those who are, this book also provides the opportunity to engage in a penetrating study of real analysis.

The companion onscreen version of this text contains hundreds of links to alternative approaches, more complete explanations and solutions to exercises; links that make it more friendly than any printed book could be. In addition, there are links to a wealth of optional material that an instructor can select for a more advanced course, and that students can use as a reference long after their first course has ended. The onscreen version also provides exercises that can be worked interactively with the help of the computer algebra systems that are bundled with Scientific Notebook.

Contents

Part I- Background Material

The emergence of rigorous calculus
Mathematical grammar
Strategies for writing proofs
Elements of set theory

Part II- Elementary Concepts of Analysis

The real number system
Elementary topology of the real line
Limits of sequences
Limits and continuity of functions
Differentiation
The exponential and logarithmic functions
The Riemann integral
Infinite series
Improper integrals
Sequences and series of functions
Calculus of a complex variable
Integration of functions of two variables
Sets of measure zero
Calculus of several variables

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Jonathan Lewin
Parution	25/02/2003
Nb. de pages	524
Format	17,5 x 24,7
Couverture	Broché
Poids	883g
Intérieur	Noir et Blanc
EAN13	9780521017183
ISBN13	978-0-521-01718-3