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Analysis Introductory Functional Analysis with Applications by Kreyszig

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  1. Jan 20, 2013 #1

    micromass

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    Table of Contents:
    Code (Text):

    [LIST]
    [*] Metric Spaces
    [LIST]
    [*] Metric Space
    [*] Further Examples of Metric Spaces
    [*] Open Set, Closed Set, Neighborhood
    [*] Convergence, Cauchy Sequence, Completeness
    [*] Examples. Completeness Proofs
    [*] Completion of Metric Spaces
    [/LIST]
    [*] Normed Spaces. Banach Spaces
    [LIST]
    [*] Vector Space
    [*] Normed Space. Banach Space
    [*] Further Properties of Normed Spaces
    [*] Finite Dimensional Normed Spaces and Subspaces
    [*] Compactness and Finite Dimension
    [*] Linear Operators
    [*] Bounded and Continuous Linear Operators
    [*] Linear Functionals
    [*] Linear Operators and Functionals on Finite Dimensional Spaces
    [*] Normed Spaces of Operators. Dual Spac
    [/LIST]
    [*] Inner Produd Spaces. Hilbert Spaces
    [LIST]
    [*] Inner Product Space. Hilbert Space
    [*] Further Properties of Inner Product Spaces
    [*] Orthogonal Complements and Direct Surns
    [*] Orthonormal Sets snd Sequences
    [*] Series Related to Orthonormal Sequences and Sets
    [*] Total Orthonormal Sets and Sequence
    [*] Legendre, Hermite and Laguerre Polynomials
    [*] Representation of Functionals on Hilbert Spaces
    [*] Hilbert-Adjoint Operator
    [*] Self-Adjoint, Unitary and Normal Operators
    [/LIST]
    [*] Fundamental Theorems for Normed and Banach Spaces
    [LIST]
    [*] Zorn's Lemma
    [*] Hahn-Banach Theorem
    [*] Hahn-Banach Theorem for Complex Vector Spaces and Normed Spaces
    [*] Application to Bounded Linear Functionals on [itex]C[a, b][/itex]
    [*] Adjoint Operator
    [*] Reflexive Spaces
    [*] Category Theorem. Uniform Boundedness Theorem
    [*] Strong and Weak Convergence
    [*] Convergence of Sequences of Operators and Functionals
    [*] Application to Summability of Sequences
    [*] Numerical Integration and Weak* Convergence
    [*] Open Mapping Theorem
    [*] Closed Linear Operators. Closed Graph Theorem
    [/LIST]
    [*] Further Applications: Banach Fixed Point Theorem
    [LIST]
    [*] Banach Fixed Point Theorem
    [*] Application of Banach's Theorem to Linear Equations
    [*] Applications of Banach's Theorem to Differential Equations
    [*] Application of Banach's Theorem to Integral Equations
    [/LIST]
    [*] Further Applications: Approximation Theory
    [LIST]
    [*] Approximation in Normed Spaces
    [*] Uniqueness. Strict Convexity
    [*] Uniform Approximation
    [*] Chebyshev Polynomials
    [*] Approximation in Hilbert Space
    [*] Splines
    [/LIST]
    [*] Spectral Theory of Linear Operators in Normed Spaces
    [LIST]
    [*] Spectral Theory in Finite Dimensional Normed Spaces
    [*] Basic Concepts
    [*] Spectral Properties of Bounded Linear Operators
    [*] Further Properties of Resolvent and Spectrum
    [*] Use of Complex Analysis in Spectral Theory
    [*] Banach Algebras
    [*] Further Properties of Banach Algebras
    [/LIST]
    [*] Compact Linear Operators on Normed Spaces and Their Spectrum
    [LIST]
    [*] Compact Linear Operators on Normed Spaces
    [*] Further Properties of Compact Linear Operators
    [*] Spectral Properties of Compact Linear Operators on Normed Spaces
    [*] Further Spectral Properties of Compact Linear Operators
    [*] Operator Equations Involving Compact Linear Operators
    [*] Further Theorems of Fredholm Type
    [*] Fredholm Alternative
    [/LIST]
    [*] Spectral Theory of Bounded Self-Adjoint Linear Operators
    [LIST]
    [*] Spectral Properties of Bounded SeIf-Adjoint Linear Operators
    [*] Further Spectral Properties of Bounded Self-Adjoint Linear Operators
    [*] Positive Operators
    [*] Square Roots of a Positive Operator
    [*] Projection Operators
    [*] Further Properties of Projections
    [*] Spectral Family
    [*] Spectral Family of a Bounded Self-Adjoint Linear Operator
    [*] Spectral Representation of Bounded Self-Adjoint Linear Operators
    [*] Extension of the Spectral Theorem to Continuous Functions
    [*] Properties of tbe Spectral Family of a Bounded Self-Adjoint Linear Operator
    [/LIST]
    [*] Unbounded Linear Operators in Hilbert Space
    [LIST]
    [*] Unbounded Linear Operators and their Hilbert-Adjoint Operators
    [*] Hilbert-Adjoint Operators, Symmetric and Self-Adjoint Linear Operators
    [*] Closed Linear Operators and Closures
    [*] Spectral Properties of Self-Adjoint Linear Operators
    [*] Spectral Representation of Unitary Operators
    [*] Spectral Representation of Self-Adjoint Linear Operators
    [*] Multiplication Operator and Differentiation Operator
    [/LIST]
    [*] Unbounded Linear Operaton in Quantum Mechanics
    [LIST]
    [*] Basic Ideas. States, Observables Position Operator
    [*] Momentum Operator. Heisenberg Uncertainty Principle
    [*] Time-Independent Schrodinger Equation
    [*] Hamilton Operator
    [*] Time- Dependent Schrodinger Equation
    [/LIST]
    [*] Appendix: Some Material for Review and Reference
    [LIST]
    [*] Sets
    [*] Mappings
    [*] Families
    [*] Equivalence Relations
    [*] Compactness
    [*] Supremum and Infimum
    [*] Cauchy Convergence Criterion
    [*] Groups
    [/LIST]
    [*] Appendix: Answers to Odd-Numbered Problems
    [*] Appendix: References
    [*] Index
    [/LIST]
     
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Feb 7, 2013 #2
    This book is great. Measure theory & topology is kept to a minimum, and there's a chapter on quantum mechanics at the end, which would probably make it better for physics than math. oh, & 900 problems too.
     
    Last edited: Feb 7, 2013
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