# Primer of Modern Analysis

Textbook

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

1. Front Matter
Pages i-xv
2. ### Part I

1. Front Matter
Pages 1-1
2. Kennan T. Smith
Pages 3-14
3. Kennan T. Smith
Pages 15-33
4. Kennan T. Smith
Pages 34-49
5. Kennan T. Smith
Pages 50-79
6. Kennan T. Smith
Pages 80-88
7. Kennan T. Smith
Pages 89-119
3. ### Part II

1. Front Matter
Pages 121-121
2. Kennan T. Smith
Pages 123-157
3. Kennan T. Smith
Pages 158-177
4. Kennan T. Smith
Pages 178-222
5. Kennan T. Smith
Pages 223-248
6. Kennan T. Smith
Pages 249-277
7. Kennan T. Smith
Pages 278-288
4. ### Part III

1. Front Matter
Pages 289-289
2. Kennan T. Smith
Pages 291-347
3. Kennan T. Smith
Pages 348-370
4. Kennan T. Smith
Pages 371-395
5. Kennan T. Smith
Pages 396-415

### Introduction

This book discusses some of the first principles of modern analysis. I t can be used for courses at several levels, depending upon the background and ability of the students. It was written on the premise that today's good students have unexpected enthusiasm and nerve. When hard work is put to them, they work harder and ask for more. The honors course (at the University of Wisconsin) which inspired this book was, I think, more fun than the book itself. And better. But then there is acting in teaching, and a typewriter is a poor substitute for an audience. The spontaneous, creative disorder that characterizes an exciting course becomes silly in a book. To write, one must cut and dry. Yet, I hope enough of the spontaneity, enough of the spirit of that course, is left to enable those using the book to create exciting courses of their own. Exercises in this book are not designed for drill. They are designed to clarify the meanings of the theorems, to force an understanding of the proofs, and to call attention to points in a proof that might otherwise be overlooked. The exercises, therefore, are a real part of the theory, not a collection of side issues, and as such nearly all of them are to be done. Some drill is, of course, necessary, particularly in the calculation of integrals.

### Keywords

Algebra Analysis Calculation Derivative Manifold Maximum Minimum calculus differential equation fixed-point theorem function geometry logarithm measure theorem

#### Authors and affiliations

1. 1.Mathematics DepartmentOregon State UniversityCorvallisUSA

### Bibliographic information

• Book Title Primer of Modern Analysis
• Authors K.T. Smith
• Series Title Undergraduate Texts in Mathematics
• DOI https://doi.org/10.1007/978-1-4612-1144-0
• Copyright Information Springer Science+Business Media New York 1983
• Publisher Name Springer, New York, NY
• eBook Packages
• Hardcover ISBN 978-0-387-90797-0
• Softcover ISBN 978-1-4612-7021-8
• eBook ISBN 978-1-4612-1144-0
• Series ISSN 0172-6056
• Edition Number 2
• Number of Pages XV, 446
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Additional Information Originally published by Bogden & Guigley, Inc.
• Topics
• Buy this book on publisher's site
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