Applied Functional Analysis

ISBN-10: 0486422585
ISBN-13: 9780486422589
Edition: 2002
Authors: D. H. Griffel
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Description: An introduction to functional analysis, this volume examines many important applications to mechanics, fluid mechanics, diffusive growth, and approximation.

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Book details

List price: $24.95
Copyright year: 2002
Publisher: Dover Publications, Incorporated
Publication date: 6/14/2002
Binding: Paperback
Pages: 390
Size: 6.06" wide x 9.21" long x 1.00" tall
Weight: 1.364
Language: English

An introduction to functional analysis, this volume examines many important applications to mechanics, fluid mechanics, diffusive growth, and approximation.

Preface
Distribution Theory and Green's Functions
Generalised Functions
The Delta Function
Basic Distribution Theory
Operations on Distributions
Convergence of Distributions
Further Developments
Fourier Series and the Poisson Sum Formula
Summary and References
Problems
Differential Equations and Green's Functions
The Integral of a Distribution
Linear Differential Equations
Fundamental Solutions of Differential Equations
Green's Functions
Applications of Green's Functions
Summary and References
Problems
Fourier Transforms and Partial Differential Equations
The Classical Fourier Transform
Distributions of Slow Growth
Generalised Fourier Transforms
Generalised Functions of Several Variables
Green's Function for the Laplacian
Green's Function for the Three-Dimensional Wave Equation
Summary and References
Problems
Banach Spaces and Fixed Point Theorems
Normed Spaces
Vector Spaces
Normed Spaces
Convergence
Open and Closed Sets
Completeness
Equivalent Norms
Summary and References
Problems
The Contraction Mapping Theorem
Operators on Vector Spaces
The Contraction Mapping Theorem
Application to Differential and Integral Equations
Nonlinear Diffusive Equilibrium
Nonlinear Diffusive Equilibrium in Three Dimensions
Summary and References
Problems
Compactness and Schauder's Theorem
Continuous Operators
Brouwer's Theorem
Compactness
Relative Compactness
Arzela's Theorem
Schauder's Theorems
Forced Nonlinear Oscillations
Swirling Flow
Summary and References
Problems
Operators in Hilbert Space
Hilbert Space
Inner Product Spaces
Orthogonal Bases
Orthogonal Expansions
The Bessel, Parseval, and Riesz-Fischer Theorems
Orthogonal Decomposition
Functionals on Normed Spaces
Functionals in Hilbert Space
Weak Convergence
Summary and References
Problems
The Theory of Operators
Bounded Operators on Normed Spaces
The Algebra of Bounded Operators
Self-Adjoint Operators
Eigenvalue Problems for Self-Adjoint Operators
Compact Operators
Summary and References
Problems
The Spectral Theorem
The Spectral Theorem
Sturm-Liouville Systems
Partial Differential Equations
The Fredholm Alternative
Projection Operators
Summary and References
Problems
Variational Methods
Positive Operators
Approximation to the First Eigenvalue
The Rayleigh-Ritz Method for Eigenvalues
The Theory of the Rayleigh-Ritz Method
Inhomogeneous Equations
Complementary Bounds
Summary and References
Problems
Further Developments
The Differential Calculus of Operators and its Applications
The Frechet Derivative
Higher Derivatives
Maxima and Minima
Linear Stability Theory
Nonlinear Stability
Bifurcation Theory
Bifurcation and Stability
Summary and References
Distributional Hilbert Spaces
The Space of Square-Integrable Distributions
Sobolev Spaces
Application to Partial Differential Equations
Summary and References
Appendices
Sets and Mappings
Sequences, Series, and Uniform Convergence
Sup and Inf
Countability
Equivalence Relations
Completion
Sturm-Liouville Systems
Fourier's Theorem
Proofs of 9.24 and 9.25
Notes on the Problems
Supplementary Problems
Symbol Index
References and Name Index
Subject Index

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