Advertisement

Real Analysis and Applications

Theory in Practice

  • Kenneth R. Davidson
  • Allan P. Donsig

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

Table of contents

  1. Front Matter
    Pages 1-10
  2. Analysis

    1. Front Matter
      Pages 1-1
    2. Kenneth R. Davidson, Allan P. Donsig
      Pages 3-8
    3. Kenneth R. Davidson, Allan P. Donsig
      Pages 9-34
    4. Kenneth R. Davidson, Allan P. Donsig
      Pages 35-47
    5. Kenneth R. Davidson, Allan P. Donsig
      Pages 48-66
    6. Kenneth R. Davidson, Allan P. Donsig
      Pages 67-93
    7. Kenneth R. Davidson, Allan P. Donsig
      Pages 94-112
    8. Kenneth R. Davidson, Allan P. Donsig
      Pages 113-141
    9. Kenneth R. Davidson, Allan P. Donsig
      Pages 142-174
    10. Kenneth R. Davidson, Allan P. Donsig
      Pages 175-186
  3. Applications

    1. Front Matter
      Pages 188-188
    2. Kenneth R. Davidson, Allan P. Donsig
      Pages 189-239
    3. Kenneth R. Davidson, Allan P. Donsig
      Pages 240-292
    4. Kenneth R. Davidson, Allan P. Donsig
      Pages 293-327
    5. Kenneth R. Davidson, Allan P. Donsig
      Pages 328-359
    6. Kenneth R. Davidson, Allan P. Donsig
      Pages 360-405
    7. Kenneth R. Davidson, Allan P. Donsig
      Pages 406-448
    8. Kenneth R. Davidson, Allan P. Donsig
      Pages 449-504
  4. Back Matter
    Pages 1-9

About this book

Introduction

This new approach to real analysis stresses the use of the subject in applications, showing how the principles and theory of real analysis can be applied in various settings. Applications cover approximation by polynomials, discrete dynamical systems, differential equations, Fourier series and physics, Fourier series and approximation, wavelets, and convexity and optimization. Each chapter has many useful exercises.

 

The treatment of the basic theory covers the real numbers, functions, and calculus, while emphasizing the role of normed vector spaces, and particularly of Rn. The applied chapters are mostly independent, giving the reader a choice of topics. This book is appropriate for students with a prior knowledge of both calculus and linear algebra who want a careful development of both analysis and its use in applications.

 

Review of the previous version of this book, Real Analysis with Real Applications:

 

"A well balanced book! The first solid analysis course, with proofs, is central in the offerings of any math.-dept.; ---and yet, the new books that hit the market don't always hit the mark: the balance between theory and applications, ---between technical proofs and intuitive ideas, ---between classical and modern subjects, and between real life exercises vs. the ones that drill a new concept. The Davidson-Donsig book is outstanding, and it does hit the mark."

 

Palle E. T. Jorgenson, Review from Amazon.com

 

Kenneth R. Davidson is University Professor of Mathematics at the University of Waterloo. Allan P. Donsig is Associate Professor of Mathematics at the University of Nebraska-Lincoln.

Keywords

Analysis Applications Real analysis calculus linear algebra linear optimization nonlinear optimization optimization

Authors and affiliations

  • Kenneth R. Davidson
    • 1
  • Allan P. Donsig
    • 2
  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Dept. MathematicsUniversity of Nebraska, LincolnLincolnU.S.A.

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-98098-0
  • Copyright Information Springer-Verlag New York 2010
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-98097-3
  • Online ISBN 978-0-387-98098-0
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site