Concepts from Tensor Analysis and Differential Geometry by Tracy Y Thomas
eBook - PDF

Concepts from Tensor Analysis and Differential Geometry by Tracy Y Thomas

  1. 322 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Concepts from Tensor Analysis and Differential Geometry by Tracy Y Thomas

About this book

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

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Yes, you can access Concepts from Tensor Analysis and Differential Geometry by Tracy Y Thomas by Tracy Y. Thomas in PDF and/or ePUB format, as well as other popular books in Technology & Engineering & Mathematical Analysis. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Front Cover
  2. Concepts From Tensor Analysis and Differential Geometry
  3. Copyright Page
  4. Contents
  5. Preface
  6. Chapter 1. Coordinate Manifolds
  7. Chapter 2. Scalars
  8. Chapter 3. Vectors and Tensors
  9. Chapter 4. A Special Skew-symmetric Tensor
  10. Chapter 5. The Vector Product. Curl of a Vector
  11. Chapter 6. Riemann Spaces
  12. Chapter 7. Affinely Connected Spaces
  13. Chapter 8. Normal Coordinates
  14. Chapter 9. General Theory of Extension
  15. Chapter 10. Absolute Differentiation
  16. Chapter 11. Differential Invariants
  17. Chapter 12. Transformation Groups
  18. Chapter 13. Euclidean Metric Space
  19. Chapter 14. Homogeneous and Isotropic Tensors
  20. Chapter 15. Curves in Space. Frenet Formulae
  21. Chapter 16. Surfaces in Space
  22. Chapter 17. Mixed Surface and Space Tensors. Coordinate Extension and Absolute Differentiation
  23. Chapter 18. Formulae of Gauss and Weingarten
  24. Chapter 19. Gaussian and Mean Curvature of a Surface
  25. Chapter 20. Equations of Gauss and Codazzi
  26. Chapter 21. Principal Curvatures and Principal Directions
  27. Chapter 22. Asymptotic Lines
  28. Chapter 23. Orthogonal Ennuples and Normal Congruences
  29. Chapter 24. Families of Parallel Surfaces
  30. Chapter 25. Developable Surfaces. Minimal Surfaces
  31. Subject Index