Item description for Postmodern Analysis (Universitext) by Hassan Azad Jurgen Jost...
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.
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Reviews - What do customers think about Postmodern Analysis (Universitext)?
describes Hilbert and Banach spaces Jan 8, 2007
The title is a trifle awkward. What would we call a later book that goes beyond postmodern analysis? The "post" is meant by Jost to differentiate this text from the generally labelled "modern analysis" of the late 19th century and continuing into the 20th century.
Labels aside, the book is a rigorous continuation of analysis. Beyond the level in Marsden's "Elementary Classical Analysis". Jost develops crucial ideas, like metric spaces, normed spaces, and what happens when we have completeness in both types, yielding Hilbert and Banach spaces. The former should be quite well known in mathematical physics, as the underlying space for quantum mechanics.
The book also explains the Lebesgue integral and topological spaces. Much of this is for the pure mathematician. But scientists can also use the sections devoted to solving partial differential equations. Though I imagine that the abstractness of the treatment might be beyond the background of many scientists.