ENGLISH

A radical approach to real analysis

By David Bressoud

Book information

Publisher
Mathematical Association of America
Year
1996
ISBN
9780883857014, 0883857014
LCC
QA300 .B685 1994
Open Library ID
OL1444572M
Language
english
Format
DJVU
Filesize
3 MB (3055706 bytes)
Series
Classroom resource materials series 2
Pages
335\335
Time added
2009-08-06 05:14:26

Description

This book is an undergraduate introduction to real analysis. Teachers can use it as a textbook for an innovative course, or as a resource for a traditional course. Students who have been through a traditional course, but do not understand what real analysis is about and why it was created, will find answers to many of their questions in this book. Although this is not a history of analysis, the author returns to the roots of the subject to make it more comprehensible. The book begins with Fourier's introduction of trigonometric series and the problems they created for the mathematicians of the early nineteenth century. Cauchy's attempts to establish a firm foundation for calculus follow, and the author considers his failures and his successes. The book culminates with Dirichlet's proof of the validity of the Fourier series expansion and explores some of the counterintuitive results Riemann and Weierstrass were led to as a result of Dirichlet's proof. Mathematica ® commands and programs are included in the exercises. However, the reader may use any mathematical tool that has graphing capabilities, including the graphing calculator.

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