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Mathematical Analysis

An Introduction

  • Andrew Browder

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

Table of contents

  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

About this book

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

  • Andrew Browder
    • 1
  1. 1.Mathematics DepartmentBrown UniversityProvidenceUSA

Bibliographic information

  • 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 Springer Book Archive
  • Print ISBN 978-1-4612-6879-6
  • Online ISBN 978-1-4612-0715-3
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site