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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.
Progress in the theory of economic equilibria and in game theory has proceeded hand in hand with that of the mathematical tools used in the field, namely nonlinear analysis and, in particular, convex analysis. Jean-Pierre Aubin, one of the leading specialists in nonlinear analysis and its application to economics, has written a rigorous and concise - yet still elementary and self-contained - textbook providing the mathematical tools needed to study optima and equilibria, as solutions to problems, arising in economics, management sciences, operations research, cooperative and non-cooperative games, fuzzy games etc. It begins with the foundations of optimization theory, and mathematical programming, and in particular convex and nonsmooth analysis. Nonlinear analysis is then presented, first game-theoretically, then in the framework of set valued analysis. These results are then applied to the main classes of economic equilibria. The book contains numerous exercises and problems: the latter allow the reader to venture into areas of nonlinear analysis that lie beyond the scope of the book and of most graduate courses.
The book contains the round table reports of the first European Congress of Mathematics, a new feature of this Congress devoted to furthering the contribution of mathematics to society and reporting on its interaction with the exact and social sciences. Topics: • Mathematics and the general public • Women and mathematics • Mathematics and educational policy • Let's cultivate mathematics! • Mathematical Europe: Myth or historical reality? • Philosophie des mathématiques : pourquoi ? comment ? • Mathématiques et sciences sociales • Mathe- matics and industry • Degree harmonization and student exchange programmes • The Pythagoras programme • Collaboration with devel- oping countries • Mathematical libraries in Europe • Mathematics and economics • Mathématiques et Chimie • Mathematics in medicine and biology. This book is also available in hardcover as Volume 121 of the series Progress in Mathematics, where it forms part of the three-volume set First European Congress of Mathematics. Volumes I (Invited Lectures Part 1) and II (Invited Lectures Part 2) of this set are also available separately as Volumes 119 and 120, respectively, of Progress in Mathematics.