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Quadratic form theory and differential equations /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
1980.
|
| Colección: | Mathematics in science and engineering ;
v. 152. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo Texto completo |
Tabla de Contenidos:
- Front Cover; Quadratic Form Theory and Differential Equations; Copyright Page; Contents; Preface; Chapter 0 A Few Introductory Remarks; Chapter 1 Introduction to Quadratic Forms and Differential Equations; 1.0 Introduction; 1.1 The Finite-Dimensional Case; 1.2 The Calculus of Variations; 1.3 Fundamental Lemmas (Integration by Parts); 1.4 Quadratic Forms and Differential Equations; Chapter 2 Abstract Theory; 2.0 Introduction; 2.1 Hilbert Space Theory; 2.2 Further Ideas of Hestenes; 2.3 Approximation Theory of Quadratic Forms; Chapter 3 The Second-Order Problem; 3.0 Introduction.
- 3.1 The Focal-Point Problem3.2 The Numerical Problem; 3.3 The Eigenvalue Problem; 3.4 The Numerical Eigenvalue Problems; 3.5 Proofs of Results; Chapter 4 The 2nth-Order Problem; 4.0 Introduction; 4.1 The Signature Theory of Lopez; 4.2 Approximation Theory; 4.3 Comparison Results; 4.4 Higher-Order Numerical Problems and Splines; Chapter 5 Elliptic Partial Differential Equations; 5.0 Introduction; 5.1 Summary; 5.2 The Numerical Problem; 5.3 Separation of Variables; Chapter 6 The Quadratic Control Problem; 6.0 Introduction; 6.1 Focal-Interval Theory of Quadratic Forms.
- 6.2 Focal Arcs of Differential Equations6.3 Two Examples; 6.4 An Approximation Theory of Focal Intervals; Postscript The Numerical Problem Revisited; 1. The x(t)x'(t) Term; 2. Cheap Boundary- Value Methods; 3. Systems; 4. Nonlinear Problems; References; Index.