ENGLISH

Practical Analysis in One Variable

By Donald Estep

Book information

Publisher
Springer
Year
2002
ISBN
9780387954844, 0387954848
Open Library ID
OL7448963M
Language
english
Format
DJVU
Filesize
4 MB (4104457 bytes)
Series
Undergraduate texts in mathematics
Edition
1
Pages
635\635
Time added
2010-02-18 13:16:04

Description

Students of analysis are often beset with frustration. They ask "Why did you bound that quantity with that other quantity?" The typical answer, "Because it works out in the proof!" is certainly true, yet wholly unsatisfactory for the student.This book begins with models, real-world problems, that originally motivated the development of analysis. The student easily grasps how, and more importantly why, quantities are bounded. The days of staring at an algebraic form for hours are gone! (Well, mostly.)Instead of the normal calculus-style, simple-to-complex development of the material, Estep introduces concepts in the natural order of the real-world problems. For example, Lipschitz continuity is introduced early to solve obvious extensions to previous problems. The mathematical idea of continuity is progressively extended and provides much of the motivation for the second half of the book.By orienting on the problems solved by analysis, Estep avoids many of the bewildering difficulties encountered in traditional introductory treatments. This is the best introductory analysis book I've seen. I'm very surprised that it hasn't received more attention.

Similar books