A First Course in Real Analysis

  • M. H. Protter
  • C. B. MorreyJr.

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

Table of contents

  1. Front Matter
    Pages i-xii
  2. M. H. Protter, C. B. Morrey Jr.
    Pages 1-30
  3. M. H. Protter, C. B. Morrey Jr.
    Pages 31-59
  4. M. H. Protter, C. B. Morrey Jr.
    Pages 60-83
  5. M. H. Protter, C. B. Morrey Jr.
    Pages 84-97
  6. M. H. Protter, C. B. Morrey Jr.
    Pages 98-129
  7. M. H. Protter, C. B. Morrey Jr.
    Pages 130-172
  8. M. H. Protter, C. B. Morrey Jr.
    Pages 173-193
  9. M. H. Protter, C. B. Morrey Jr.
    Pages 194-209
  10. M. H. Protter, C. B. Morrey Jr.
    Pages 210-261
  11. M. H. Protter, C. B. Morrey Jr.
    Pages 262-281
  12. M. H. Protter, C. B. Morrey Jr.
    Pages 282-299
  13. M. H. Protter, C. B. Morrey Jr.
    Pages 300-321
  14. M. H. Protter, C. B. Morrey Jr.
    Pages 322-331
  15. M. H. Protter, C. B. Morrey Jr.
    Pages 332-364
  16. M. H. Protter, C. B. Morrey Jr.
    Pages 365-403
  17. M. H. Protter, C. B. Morrey Jr.
    Pages 404-482
  18. Back Matter
    Pages 483-510

About this book

Introduction

The first course in analysis which follows elementary calculus is a critical one for students who are seriously interested in mathematics. Traditional advanced calculus was precisely what its name indicates-a course with topics in calculus emphasizing problem solving rather than theory. As a result students were often given a misleading impression of what mathematics is all about; on the other hand the current approach, with its emphasis on theory, gives the student insight in the fundamentals of analysis. In A First Course in Real Analysis we present a theoretical basis of analysis which is suitable for students who have just completed a course in elementary calculus. Since the sixteen chapters contain more than enough analysis for a one year course, the instructor teaching a one or two quarter or a one semester junior level course should easily find those topics which he or she thinks students should have. The first Chapter, on the real number system, serves two purposes. Because most students entering this course have had no experience in devising proofs of theorems, it provides an opportunity to develop facility in theorem proving. Although the elementary processes of numbers are familiar to most students, greater understanding of these processes is acquired by those who work the problems in Chapter 1. As a second purpose, we provide, for those instructors who wish to give a comprehen­ sive course in analysis, a fairly complete treatment of the real number system including a section on mathematical induction.

Keywords

Analysis Calc Differentialrechnung Impress Integralrechnung boundary element method calculus mathematics problem solving proving real analysis real number system theorem theorem proving

Authors and affiliations

  • M. H. Protter
    • 1
  • C. B. MorreyJr.
    • 1
  1. 1.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-9990-6
  • Copyright Information Springer-Verlag New York 1977
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4615-9992-0
  • Online ISBN 978-1-4615-9990-6
  • Series Print ISSN 0172-6056
  • About this book