Functional Analysis in Mechanics

  • Leonid P. Lebedev
  • Iosif I. Vorovich
  • Michael J. Cloud
Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Leonid P. Lebedev, Iosif I. Vorovich, Michael J. Cloud
    Pages 9-113
  3. Leonid P. Lebedev, Iosif I. Vorovich, Michael J. Cloud
    Pages 115-175
  4. Leonid P. Lebedev, Iosif I. Vorovich, Michael J. Cloud
    Pages 177-224
  5. Leonid P. Lebedev, Iosif I. Vorovich, Michael J. Cloud
    Pages 225-264
  6. Back Matter
    Pages 265-308

About this book

Introduction

This book offers a brief, practically complete, and relatively simple introduction to functional analysis. It also illustrates the application of functional analytic methods to the science of continuum mechanics. Abstract but powerful mathematical notions are tightly interwoven with physical ideas in the treatment of nontrivial boundary value problems for mechanical objects.

 

This second edition includes more extended coverage of the classical and abstract portions of functional analysis. Taken together, the first three chapters now constitute a regular text on applied functional analysis. This potential use of the book is supported by a significantly extended set of exercises with hints and solutions. A new appendix, providing a convenient listing of essential inequalities and imbedding results, has been added.

 

The book should appeal to graduate students and researchers in physics, engineering, and applied mathematics.

 

Reviews of first edition:

 

"This book covers functional analysis and its applications to continuum mechanics. The presentation is concise but complete, and is intended for readers in continuum mechanics who wish to understand the mathematical underpinnings of the discipline. . . . Detailed solutions of the exercises are provided in an appendix." (L’Enseignment Mathematique, Vol. 49 (1-2), 2003)

 

"The reader comes away with a profound appreciation both of the physics and its importance, and of the beauty of the functional analytic method, which, in skillful hands, has the power to dissolve and clarify these difficult problems as peroxide does clotted blood. Numerous exercises . . . test the reader’s comprehension at every stage. Summing Up: Recommended." (F. E. J. Linton, Choice, September, 2003)

Keywords

Banach–Steinhaus Principle Metric Spaces Von Karman Equations

Authors and affiliations

  • Leonid P. Lebedev
    • 1
  • Iosif I. Vorovich
    • 2
  • Michael J. Cloud
    • 3
  1. 1.Dept of Mathematics & MechanicsRostov State UniversityRostov on DonRussia
  2. 2.Dept. Mathematics & MechanicsSouthern Federal UniversityRostov-on-DonRussia
  3. 3., Department of EngineeringLawrence Technological UniversitySouthfieldUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-5868-5
  • Copyright Information Springer Science+Business Media, LLC 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-5867-8
  • Online ISBN 978-1-4614-5868-5
  • Series Print ISSN 1439-7382
  • About this book