Nonlinear Functional Analysis and Its Applications: II/ A: Linear Monotone Operators (Nonlinear Functional Analysis & Its Applications) 1990th Edition by E. Zeidler (PDF)

Description

This is the second of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self -contained and accessible to the nonspecialist. Part II concerns the theory of monotone operators. It is divided into two subvolumes, II/A and II/B, which form a unit. The present Part II/A is devoted to linear monotone operators. It serves as an elementary introduction to the modern functional analytic treatment of variational problems, integral equations, and partial differential equations of elliptic, parabolic and hyperbolic type. This book also represents an introduction to numerical functional analysis with applications to the Ritz method along with the method of finite elements, the Galerkin methods, and the difference method. Many exercises complement the text. The theory of monotone operators is closely related to Hilbert’s rigorous justification of the Dirichlet principle, and to the 19th and 20th problems of Hilbert which he formulated in his famous Paris lecture in 1900, and which strongly influenced the development of analysis in the twentieth century.

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Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Hats off to Prof. Zeidler for his 5 vol series on non-linear FA. Complete, comprehensive, full of motivation, and with abundant examples and applications. Extensive historical notes are an added bonus. Where else would you read that modeling a nuclear reactor can involve solving of 10^5 simultaneous elliptic PDEs?!

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