Introduction to Real Analysis, Wm C Bauldry

The Text

From the Preface

Elementary calculus students develop intuitive concepts of limits, derivatives, and integrals. While adequate for most, those who teach calculus need a much deeper understanding. The purpose of this book is to present an introductory course in analysis, rebuilding intuitive understandings with more rigorous foundations, with emphases chosen for the practicing secondary teacher. The text is based on a one semester, four credit hour, graduate course in our Masters in Mathematics with a concentration in Secondary Education program. Since we wish to cover a significant amount of material in one semester, some topics will necessarily be given short attention and others are not covered. This reduction allows us to introduce Lebesgue measure and integration. The last chapter presents a set of special topics with ties to elementary calculus that can be used as student projects. These topics can be studied in more depth if time permits.

Abbreviated Table of Contents

Chapter 1. Elementary Calculus
Chapter 2. Introduction to Real Analysis
Chapter 3. A Brief Introduction to Lebesgue Theory
Chapter 4. Special Topics
Appendices. Definitions and Theorems of Elementary Real Analysis, A Very Brief Calculus Chronology, Projects in Real Analysis
Bibliography
Index

View the Full TOC.

Presentations

ICTCM 20: “Using Maple in Advanced Calculus and Modern Algebra” — WmCB
Abstract: We present a discussion and demonstration of enhancing upper-level courses such as Modern Algebra and Advanced Calculus with Maple. Worksheets with embedded components that allow students to focus on concepts, rather than syntax, are highlighted.
| pdf (pdf) | Maple Demo (Maple 12 file) | Class material archives |
ICTCM 19: “Using Maple in an Analysis for Teachers Graduate Course” — WmCB
Abstract: We will discuss how Maple can be used to enhance a masters level Analysis for Teachers course. Both aspects will be considered: Maple for the student’s use and Maple for the student’s student use.
| Slides (pdf) | Class notes (pdf) | Limits (Maple file) | Class material archives |