# Mathematical Analysis

## An Introduction

Textbook

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

1. Front Matter
Pages i-xiv
2. Andrew Browder
Pages 1-27
3. Andrew Browder
Pages 28-54
4. Andrew Browder
Pages 55-73
5. Andrew Browder
Pages 74-97
6. Andrew Browder
Pages 98-122
7. Andrew Browder
Pages 123-154
8. Andrew Browder
Pages 155-174
9. Andrew Browder
Pages 175-200
10. Andrew Browder
Pages 201-222
11. Andrew Browder
Pages 223-252
12. Andrew Browder
Pages 253-268
13. Andrew Browder
Pages 269-284
14. Andrew Browder
Pages 285-296
15. Andrew Browder
Pages 297-321
16. Back Matter
Pages 323-335

### Introduction

This is a textbook suitable for a year-long course in analysis at the ad­ vanced undergraduate or possibly beginning-graduate level. It is intended for students with a strong background in calculus and linear algebra, and a strong motivation to learn mathematics for its own sake. At this stage of their education, such students are generally given a course in abstract algebra, and a course in analysis, which give the fundamentals of these two areas, as mathematicians today conceive them. Mathematics is now a subject splintered into many specialties and sub­ specialties, but most of it can be placed roughly into three categories: al­ gebra, geometry, and analysis. In fact, almost all mathematics done today is a mixture of algebra, geometry and analysis, and some of the most in­ teresting results are obtained by the application of analysis to algebra, say, or geometry to analysis, in a fresh and surprising way. What then do these categories signify? Algebra is the mathematics that arises from the ancient experiences of addition and multiplication of whole numbers; it deals with the finite and discrete. Geometry is the mathematics that grows out of spatial experience; it is concerned with shape and form, and with measur­ ing, where algebra deals with counting.

### Keywords

Derivative Fourier series Riemann integral calculus compactness differential equation exponential function mean value theorem measure

#### Authors and affiliations

1. 1.Mathematics DepartmentBrown UniversityProvidenceUSA

### Bibliographic information

• Book Title Mathematical Analysis
• Book Subtitle An Introduction
• Authors Andrew Browder
• Series Title Undergraduate Texts in Mathematics
• DOI https://doi.org/10.1007/978-1-4612-0715-3
• Copyright Information Springer-Verlag New York, Inc. 1996
• Publisher Name Springer, New York, NY
• eBook Packages
• Hardcover ISBN 978-0-387-94614-6
• Softcover ISBN 978-1-4612-6879-6
• eBook ISBN 978-1-4612-0715-3
• Series ISSN 0172-6056
• Edition Number 1
• Number of Pages XIV, 335
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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