Ebook: Nonlinear Functional Analysis and Its Applications: II/ A: Linear Monotone Operators

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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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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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.
Content:
Front Matter....Pages i-xviii
Front Matter....Pages 1-14
Variational Problems, the Ritz Method, and the Idea of Orthogonality....Pages 15-100
The Galerkin Method for Differential and Integral Equations, the Friedrichs Extension, and the Idea of Self-Adjointness....Pages 101-191
Difference Methods and Stability....Pages 192-223
Front Matter....Pages 225-227
Auxiliary Tools and the Convergence of the Galerkin Method for Linear Operator Equations....Pages 229-313
Hilbert Space Methods and Linear Elliptic Differential Equations....Pages 314-401
Hilbert Space Methods and Linear Parabolic Differential Equations....Pages 402-451
Hilbert Space Methods and Linear Hyperbolic Differential Equations....Pages 452-467

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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.
Content:
Front Matter....Pages i-xviii
Front Matter....Pages 1-14
Variational Problems, the Ritz Method, and the Idea of Orthogonality....Pages 15-100
The Galerkin Method for Differential and Integral Equations, the Friedrichs Extension, and the Idea of Self-Adjointness....Pages 101-191
Difference Methods and Stability....Pages 192-223
Front Matter....Pages 225-227
Auxiliary Tools and the Convergence of the Galerkin Method for Linear Operator Equations....Pages 229-313
Hilbert Space Methods and Linear Elliptic Differential Equations....Pages 314-401
Hilbert Space Methods and Linear Parabolic Differential Equations....Pages 402-451
Hilbert Space Methods and Linear Hyperbolic Differential Equations....Pages 452-467
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