Functional analysis in modern applied mathematics /

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrang...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Curtain, Ruth F.
Otros Autores: Pritchard, A. J.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: London ; New York : Academic Press, 1977.
Colección:Mathematics in science and engineering ; v. 132.
Temas:
Functional analysis.
Analyse fonctionnelle.
MATHEMATICS > Functional Analysis.
Functional analysis
Analytische ruimten.
Functionaalanalyse.
Electronic resource.
Acceso en línea:Texto completo
Texto completo
Tabla de Contenidos:
  • Cover13;
  • Functional Analysis in Modern Applied Mathematics
  • Copyright Page
  • Contents
  • Introduction
  • PART I: Basic Functional Analysis
  • Chapter 1. NORMED LINEAR SPACES
  • Chapter 2. INTEGRATION THEORY FOR REAL-VALUED FUNCTIONS
  • Chapter 3. LINEAR TRANSFORMATIONS
  • Chapter 4. HILBERT SPACES
  • Chapter 5. PROBABILITY THEORY
  • Chapter 6. CALCULUS IN BANACH SPACES
  • Chapter 7. TOPOLOGICAL SPACES
  • Part II: Analysis of Abstract Equations
  • Chapter 8. DIFFERENTIAL EQUATIONS
  • 8.1 Ordinary differential equations
  • 8.2 Stochastic differential equations
  • 8.3 Differential delay equations
  • 8.4 Partial differential equations
  • 8.5 Abstract equations
  • 8.6 Semigroup theory
  • 8.7 Solution of inhomogeneous abstract evolution equations
  • Chapter 9. SPECTRAL THEORY AND APPLICATIONS
  • 9.1 Spectral theory in finite dimensions
  • 9.2 Spectrum of closed linear operators on a normed linear space
  • 9.3 Spectral theory for compact normal operators
  • 9.4 Spectral decomposition for unbounded linear operators
  • Part III: Applications
  • Chapter 10. STABILITY THEORY
  • 10.1 Liapunov stability for ordinary differential equations
  • 10.2 Stability properties of operators : perturbation theory
  • Chapter 11. LINEAR SYSTEMS THEORY
  • 11.1 Controllability
  • 11.2 Stability
  • 11.3 Observability
  • 11.4 Linear quadratic control problems
  • 11.5 Filtering
  • 11.6 Time optimal control
  • Chapter 12. OPTIMIZATION PROBLEMS
  • 12.1 Minimization of coercive bilinear forms
  • 12.2 Least squares minimization in a Hilbert space
  • 12.3 Unconstrained Calculus of Variations problems
  • 12.4 Minimization under equality constraints
  • 12.5 Minimization with inequality constraints
  • 12.6 Optimal control theory
  • Chapter 13. NUMERICAL METHODS
  • 13.1 General principles and introduction
  • 13.2 Linear equations
  • 13.3 Nonlinear equations
  • 13.4 Approximation theory
  • 13.5 Numerical solution of optimization problems
  • Chapter 14. INFINITE DIMENSIONAL LINEAR SYSTEMS THEORY
  • 14.1 Controllability
  • 14.2 Observability
  • 14.3 The quadratic cost control problem for evolution equations
  • 14.4 A direct approach to the quadratic cost control problem
  • INDEX.

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