Postmodern Analysis

Postmodern Analysis
Jurgen Jost (Auteur), H. Azad (Traduction)

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Description du produit

This is an introduction to advanced analysis at the beginning graduate level that blends a modern presentation with concrete examples and applications, in particular in the areas of calculus of variations and partial differential equations. The book does not strive for abstraction for its own sake, but tries rather to impart a working knowledge of the key methods of contemporary analysis, in particular those that are also relevant for application in physics. It provides a streamlined and quick introduction to the fundamental concepts of Banach space and Lebesgue integration theory and the basic notions of the calculus of variations, including Sobolev space theory. The new edition contains additional material on the qualitative behavior of solutions of ordinary differential equations, some further details on Lp and Sobolev functions, partitions of unity and a brief introduction to abstract measure theory. From the reviews: "...Well thought out concept. Provides students at masterÆs level, both a revision and a continuation of their undergraduate analysis lectures. New elements of advanced analysis are motivated by their applications to variational problems and elliptic PDE, thus illustrating their significance in the important area of current mathematics. The book will serve some readers seeking to deepen their mathematical knowledge, it is however designed to arouse curiosity for one of the most attractive fields of mathematics. ..." --Heinrich Begehr, Mathematische Semesterberichte 1999 (translated by Catriona M. Byrne)