![Concepts from Tensor Analysis and Differential Geometry by Tracy Y Thomas](https://img.perlego.com/book-covers/1857395/9780080957784_300_450.webp)
Concepts from Tensor Analysis and Differential Geometry by Tracy Y Thomas
Tracy Y. Thomas
- 322 Seiten
- English
- PDF
- Über iOS und Android verfügbar
Concepts from Tensor Analysis and Differential Geometry by Tracy Y Thomas
Tracy Y. Thomas
Über dieses Buch
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-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
Häufig gestellte Fragen
Information
Inhaltsverzeichnis
- Front Cover
- Concepts From Tensor Analysis and Differential Geometry
- Copyright Page
- Contents
- Preface
- Chapter 1. Coordinate Manifolds
- Chapter 2. Scalars
- Chapter 3. Vectors and Tensors
- Chapter 4. A Special Skew-symmetric Tensor
- Chapter 5. The Vector Product. Curl of a Vector
- Chapter 6. Riemann Spaces
- Chapter 7. Affinely Connected Spaces
- Chapter 8. Normal Coordinates
- Chapter 9. General Theory of Extension
- Chapter 10. Absolute Differentiation
- Chapter 11. Differential Invariants
- Chapter 12. Transformation Groups
- Chapter 13. Euclidean Metric Space
- Chapter 14. Homogeneous and Isotropic Tensors
- Chapter 15. Curves in Space. Frenet Formulae
- Chapter 16. Surfaces in Space
- Chapter 17. Mixed Surface and Space Tensors. Coordinate Extension and Absolute Differentiation
- Chapter 18. Formulae of Gauss and Weingarten
- Chapter 19. Gaussian and Mean Curvature of a Surface
- Chapter 20. Equations of Gauss and Codazzi
- Chapter 21. Principal Curvatures and Principal Directions
- Chapter 22. Asymptotic Lines
- Chapter 23. Orthogonal Ennuples and Normal Congruences
- Chapter 24. Families of Parallel Surfaces
- Chapter 25. Developable Surfaces. Minimal Surfaces
- Subject Index