# A First Course in Real Analysis

• Sterling K. Berberian
Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

1. Front Matter
Pages i-xi
2. Sterling K. Berberian
Pages 1-14
3. Sterling K. Berberian
Pages 15-32
4. Sterling K. Berberian
Pages 33-55
5. Sterling K. Berberian
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12. Sterling K. Berberian
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13. Back Matter
Pages 220-240

### Introduction

Mathematics is the music of science, and real analysis is the Bach of mathematics. There are many other foolish things I could say about the subject of this book, but the foregoing will give the reader an idea of where my heart lies. The present book was written to support a first course in real analysis, normally taken after a year of elementary calculus. Real analysis is, roughly speaking, the modern setting for Calculus, "real" alluding to the field of real numbers that underlies it all. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.) readily derived from the real numbers; a first course in real analysis traditionally places the emphasis on real-valued functions defined on sets of real numbers. The agenda for the course: (1) start with the axioms for the field ofreal numbers, (2) build, in one semester and with appropriate rigor, the foun­ dations of calculus (including the "Fundamental Theorem"), and, along the way, (3) develop those skills and attitudes that enable us to continue learning mathematics on our own. Three decades of experience with the exercise have not diminished my astonishment that it can be done.

### Keywords

Finite Mean value theorem Rack Riemann integral boundary element method calculus character derivative form function proof real analysis sets system theorem

#### Authors and affiliations

• Sterling K. Berberian
• 1
1. 1.Department of MathematicsThe University of Texas at AustinAustinUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4419-8548-4
• Copyright Information Springer-Verlag New York, Inc. 1994
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4612-6433-0
• Online ISBN 978-1-4419-8548-4
• Series Print ISSN 0172-6056
• Buy this book on publisher's site