Functional Analysis in Mechanics

Buch | Hardcover
310 Seiten
2012 | 2nd ed. 2013
Springer-Verlag New York Inc.
978-1-4614-5867-8 (ISBN)

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Functional Analysis in Mechanics - Leonid P. Lebedev, Iosif I. Vorovich, Michael J. Cloud
106,99 inkl. MwSt
Fully supported with underlying mechanical concepts, this revised new edition includes exercises and examples throughout in its concise and accessible introduction to functional analysis, including new material on essential inequalities and imbedding results.
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)

Introduction.- Metric, Banach, and Hilbert Spaces.- Mechanics Problems from the Functional Analysis Viewpoint.- Some Spectral Problems of Mechanics.- Elements of Nonlinear Functional Analysis.- Summary of Inequalities and Imbeddings.- Hints for Selected Problems.- References.- In Memoriam: Iosif I. Vorovich.- Index.-

Reihe/Serie Springer Monographs in Mathematics
Zusatzinfo X, 310 p.
Verlagsort New York, NY
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
Naturwissenschaften Physik / Astronomie Mechanik
Technik Maschinenbau
Schlagworte Banach-Steinhaus Principle • Metric Spaces • Von Karman equations
ISBN-10 1-4614-5867-6 / 1461458676
ISBN-13 978-1-4614-5867-8 / 9781461458678
Zustand Neuware
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