Closer and Closer: Introducing Real Analysis

by Schumacher, Carol S.

• ISBN13: 9780763735937
• ISBN10: 0763735930
• Format: Paperback
• Copyright: 2007-07-16
• Publisher: Jones & Bartlett Learning

Summary

Closer and Closer is the ideal first introduction to real analysis for upper-level undergraduate Math majors. The text is divided into two main parts; the core material of the subject is covered in Chapters 1-12, and a series of cases, examples, applications, and projects, collectively called Excursions form the second half of the book. These Excursions are designed to bring the concepts of real analysis to light and to allow students to work through numerous interesting problems with ease.

Table of Contents

Basic building blocks	p. 9
The real numbers	p. 37
Measuring distances	p. 63
Sets and limits	p. 73
Continuity	p. 105
Real-valued functions	p. 119
Completeness	p. 131
Compactness	p. 135
Connectedness	p. 151
Differentiation of functions of one real variable	p. 159
Iteration and the contraction mapping theorem	p. 189
The riemann integral	p. 209
Sequences of functions	p. 237
Differentiating f : R[superscript n] [approaches] R[superscript m]	p. 257
Truth and provability	p. 293
Number properties	p. 295
Exponents	p. 298
Sequences in R and R[superscript n]	p. 307
Limits of functions from R to R	p. 319
Doubly indexed sequences	p. 325
Subsequences and convergence	p. 330
Series of real numbers	p. 334
Probing the definition of the riemann integral	p. 358
Power series	p. 363
Everywhere continuous, nowhere differentiable	p. 374
Newton's method	p. 380
The implicit function theorem	p. 390
Spaces of continuous 'functions	p. 408
Solutions to differential equations	p. 421
Table of Contents provided by Blackwell. All Rights Reserved.