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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 third edition contains new material on further important tool in analysis, namely cover theorems. Useful references for such results and further properties of various classes of weakly differential functions are added. And finally, misprints and minor inconsistencies have been corrected.
π SIMILAR VOLUMES
The revised and enlarged third edition of this successful book presents a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied and updated applications.Β In an effort to make the book more useful for a diverse readership, updated modern examp
Variational principles for generalized Korteweg-de Vries equation and nonlinear Schrβ¬ o odingerΓs equation are obtained by the semi-inverse method. The most interesting features of the proposed method are its extreme simplicity and concise forms of variational functionals for a wide range of nonline