Analysis

From Concepts to Applications

  • Jean-Paul Penot

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Jean-Paul Penot
    Pages 1-50
  3. Jean-Paul Penot
    Pages 51-96
  4. Jean-Paul Penot
    Pages 97-184
  5. Jean-Paul Penot
    Pages 185-218
  6. Jean-Paul Penot
    Pages 219-316
  7. Jean-Paul Penot
    Pages 317-397
  8. Jean-Paul Penot
    Pages 399-440
  9. Jean-Paul Penot
    Pages 441-517
  10. Jean-Paul Penot
    Pages 519-595
  11. Jean-Paul Penot
    Pages 597-645
  12. Back Matter
    Pages 647-669

About this book

Introduction

This textbook covers the main results and methods of real analysis in a single volume. Taking a progressive approach to equations and transformations, this book starts with the very foundations of real analysis (set theory, order, convergence, and measure theory) before presenting powerful results that can be applied to concrete problems.

In addition to classical results of functional analysis, differential calculus and integration, Analysis discusses topics such as convex analysis, dissipative operators and semigroups which are often absent from classical treatises. Acknowledging that analysis has significantly contributed to the understanding and development of the present world, the book further elaborates on techniques which pervade modern civilization, including wavelets in information theory, the Radon transform in medical imaging and partial differential equations in various mechanical and physical phenomena.

Advanced undergraduate and graduate students, engineers as well as practitioners wishing to familiarise themselves with concepts and applications of analysis will find this book useful. With its content split into several topics of interest, the book’s style and layout make it suitable for use in several courses, while its self-contained character make it appropriate for self-study.

Keywords

convex analysis differential calculus evolution problems functional analysis integration partial differential equations

Authors and affiliations

  • Jean-Paul Penot
    • 1
  1. 1.Université Pierre et Marie CurieParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-32411-1
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-32409-8
  • Online ISBN 978-3-319-32411-1
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book