ABSTRACT

Students preparing for courses in real analysis often encounter either very exacting theoretical treatments or books without enough rigor to stimulate an in-depth understanding of the subject. Further complicating this, the field has not changed much over the past 150 years, prompting few authors to address the lackluster or overly complex dichotom

chapter 1|38 pages

Logic and Set Theory

chapter 2|36 pages

Number Systems

chapter 3|20 pages

Sequences

chapter 4|34 pages

Series of Numbers

chapter 5|24 pages

Basic Topology

chapter 6|28 pages

Limits and Continuity of Functions

chapter 7|24 pages

Differentiation of Functions

chapter 8|32 pages

The Integral

chapter |20 pages

Sequences and Series of Functions

chapter 10|28 pages

Elementary Transcendental Functions

chapter 12|38 pages

Introduction to Harmonic Analysis

chapter 13|34 pages

Functions of Several Variables

chapter 14|42 pages

Advanced Topics

chapter 15|24 pages

A Glimpse of Wavelet Theory