Applied Functional Analysis
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Beschreibung
A novel, practical introduction to functional analysis
In the twenty years since the first edition of Applied Functional Analysis was published, there has been an explosion in the number of books on functional analysis. Yet none of these offers the unique perspective of this new edition. Jean-Pierre Aubin updates his popular reference on functional analysis with new insights and recent discoveries-adding three new chapters on set-valued analysis and convex analysis, viability kernels and capture basins, and first-order partial differential equations. He presents, for the first time at an introductory level, the extension of differential calculus in the framework of both the theory of distributions and set-valued analysis, and discusses their application for studying boundary-value problems for elliptic and parabolic partial differential equations and for systems of first-order partial differential equations.
To keep the presentation concise and accessible, Jean-Pierre Aubin introduces functional analysis through the simple Hilbertian structure. He seamlessly blends pure mathematics with applied areas that illustrate the theory, incorporating a broad range of examples from numerical analysis, systems theory, calculus of variations, control and optimization theory, convex and nonsmooth analysis, and more. Finally, a summary of the essential theorems as well as exercises reinforcing key concepts are provided. Applied Functional Analysis, Second Edition is an excellent and timely resource for both pure and applied mathematicians.
Mit diesem Buch verfolgt der Autor zwei Ziele: Erstens will er in die wichtigsten algebraischen Strukturen einführen, zweitens will er den Studenten helfen, ihre Fähigkeiten zum Arbeiten mit abstrakten Begriffen zu vervollkommnen. Die Kerngedanken werden in den ersten sechs Kapiteln vorgestellt, während der zweite Teil des Buches flexibel angelegt ist. Didaktisch sehr sinnvoll ist die beigefügte Anleitung zum Lesen, Analysieren und Aufstellen von Sätzen und Beweisen. (12/99)
Autor*in
Jean-Pierre Aubin
Themen in »Applied Functional Analysis«
Complex & Functional Analysis Funktionalanalysis Komplexe Analysis u. Funktionalanalysis Mathematics Mathematik
Stimmen zu »Applied Functional Analysis«
"Reflects author's background in numerical analysis, partial differential equations, and mathematical economics.... Good exercises." (American Mathematical Monthly, November 2001)
"The second edition has made some additions and some deletions..." (Zentralblatt MATH, Vol. 946, No. 21)
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"...full of interesting and/or amazing comments...an original and valuable contribution to functional analysis..." (Bulletin of The Belgian Mathematical Society, Vol.11, No.4, 2004)
"Reflects author's background in numerical analysis, partial differential equations, and mathematical economics.... Good exercises." (American Mathematical Monthly, November 2001)
"The second edition has made some additions and some deletions..." (Zentralblatt MATH, Vol. 946, No. 21)
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