© 2016


From Concepts to Applications

  • Presents results of analysis that can be applied to a wealth of concrete problems

  • Starts from the foundations and leads to powerful results

  • Treats less traditional topics such as convex analysis, monotone operators, and the Laplace and Radon transforms


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


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.


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

Authors and affiliations

  1. 1.Université Pierre et Marie CurieParisFrance

About the authors

Jean-Paul Penot has published about 250 research articles and two books, including Calculus Without Derivatives, Graduate Texts in Mathematics Volume 266, Springer. He has taught in Paris (France), Sherbrooke (Canada), Pau (France) and participated in numerous conferences. His research interests include global analysis, optimization, convex analysis and nonsmooth analysis.

Bibliographic information

Industry Sectors
Finance, Business & Banking


“The topics it deals with are treated rather deeply, much beyond the needs required by their applicability. As a result, this book may be very useful to a large variety of readers, including professional mathematicians, graduate students and researchers and practitioners in many fields.  … In summary, this is an excellent book. … I recommend it to every mathematical analyst, every applied mathematician, and every other user of mathematical analysis.” (Juan Enrique Martínez-Legaz, Mathematical Reviews, 2018)

“This textbook is mainly intended for advanced undergraduate and graduate students, engineers as well as practitioners who want to be familiar with concepts and applications of analysis. … The book it suitable for use in several courses, and its self-contained character make it appropriate for self-study.” (Petr Gurka, zbMATH, Vol. 1366.26002, 2017)