Concepts from Tensor Analysis and Differential Geometry by Tracy Y Thomas

Tracy Y. Thomas

• Editorial: Elsevier Science
• Año: 2000
• ISBN:
  9780080957784
• Categoría: Technologie et ingénierie
• Categoría: Génie mécanique

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

Índice

• 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