Concepts From Tensor Analysis And Differential Geometry

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Concepts From Tensor Analysis And Differential Geometry By Tracy Y Thomas

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Author :
language : en
Publisher: Elsevier
Release Date : 2000-04-01

Concepts From Tensor Analysis And Differential Geometry By Tracy Y Thomas written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Technology & Engineering categories.

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

Concepts From Tensor Analysis And Differential Geometry

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Author : Tracy Yerkes Thomas
language : en
Publisher:
Release Date : 2013-08

Concepts From Tensor Analysis And Differential Geometry written by Tracy Yerkes Thomas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08 with categories.

Concepts From Tensor Analysis And Differential Geometry

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Author : Tracy Y. Thomas
language : en
Publisher: Elsevier
Release Date : 2016-06-03

Concepts From Tensor Analysis And Differential Geometry written by Tracy Y. Thomas and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-03 with Mathematics categories.

Concepts from Tensor Analysis and Differential Geometry discusses coordinate manifolds, scalars, vectors, and tensors. The book explains some interesting formal properties of a skew-symmetric tensor and the curl of a vector in a coordinate manifold of three dimensions. It also explains Riemann spaces, affinely connected spaces, normal coordinates, and the general theory of extension. The book explores differential invariants, transformation groups, Euclidean metric space, and the Frenet formulae. The text describes curves in space, surfaces in space, mixed surfaces, space tensors, including the formulae of Gaus and Weingarten. It presents the equations of two scalars K and Q which can be defined over a regular surface S in a three dimensional Riemannian space R. In the equation, the scalar K, which is an intrinsic differential invariant of the surface S, is known as the total or Gaussian curvature and the scalar U is the mean curvature of the surface. The book also tackles families of parallel surfaces, developable surfaces, asymptotic lines, and orthogonal ennuples. The text is intended for a one-semester course for graduate students of pure mathematics, of applied mathematics covering subjects such as the theory of relativity, fluid mechanics, elasticity, and plasticity theory.

Computational Methods For Modeling Of Nonlinear Systems

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Author : Anatoli Torokhti
language : en
Publisher: Elsevier Science Limited
Release Date : 1961

Computational Methods For Modeling Of Nonlinear Systems written by Anatoli Torokhti and has been published by Elsevier Science Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Mathematics categories.

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; and methods 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 particular branches, 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

Concepts From Tensor Analysis And Differential Geometry

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Author : Tracy Yerkes Thomas
language : it
Publisher:
Release Date : 1961

Concepts From Tensor Analysis And Differential Geometry written by Tracy Yerkes Thomas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with categories.

Concepts From Tensor Analysis And Differential Geometry

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Author : Charles Louis Kuhn
language : en
Publisher:
Release Date : 1965

Concepts From Tensor Analysis And Differential Geometry written by Charles Louis Kuhn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with categories.

Concepts From Tensor Analysis And Differential Geometry Second Edition

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Author : Tracy Yerkes THOMAS
language : en
Publisher:
Release Date : 1965

Concepts From Tensor Analysis And Differential Geometry Second Edition written by Tracy Yerkes THOMAS and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with categories.

Textbook Of Tensor Calculus And Differential Geometry And Their Applications

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Author : Quddus Khan
language : en
Publisher: Misha Books
Release Date : 2020-12-29

Textbook Of Tensor Calculus And Differential Geometry And Their Applications written by Quddus Khan and has been published by Misha Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-29 with Mathematics categories.

This book is intended to serve as a Textbook for Undergraduate and Post - graduate students of Mathematics. It will be useful to the researchers working in the field of Differential geometry and its applications to general theory of relativity and other applied areas. It will also be helpful in preparing for the competitive examinations like IAS, IES, NET, PCS, and UP Higher Education exams. The text starts with a chapter on Preliminaries discussing basic concepts and results which would be taken for general later in the subsequent chapters of this book. This is followed by the Study of the Tensors Algebra and its operations and types, Christoffel's symbols and its properties, the concept of covariant differentiation and its properties, Riemann's symbols and its properties, and application of tensor in different areas in part – I and the study of the Theory of Curves in Space, Concepts of a Surface and Fundamental forms, Envelopes and Developables, Curvature of Surface and Lines of Curvature, Fundamental Equations of Surface Theory, Theory of Geodesics, Differentiable Manifolds and Riemannian Manifold and Application of Differential Geometry in Part –II. KEY FEATURES: Provides basic Concepts in an easy to understand style; Presentation of the subject in a natural way; Includes a large number of solved examples and illuminating illustrations; Exercise questions at the end of the topic and at the end of each chapter; Proof of the theorems are given in an easy to understand style; Neat and clean figures are given at appropriate places; Notes and remarks are given at appropriate places.

Introduction To Differential Geometry Of Space Curves And Surfaces

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Author : Taha Sochi
language : en
Publisher: Taha Sochi
Release Date : 2022-09-14

Introduction To Differential Geometry Of Space Curves And Surfaces written by Taha Sochi and has been published by Taha Sochi this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-14 with Mathematics categories.

This book is about differential geometry of space curves and surfaces. The formulation and presentation are largely based on a tensor calculus approach. It can be used as part of a course on tensor calculus as well as a textbook or a reference for an intermediate-level course on differential geometry of curves and surfaces. The book is furnished with an index, extensive sets of exercises and many cross references, which are hyperlinked for the ebook users, to facilitate linking related concepts and sections. The book also contains a considerable number of 2D and 3D graphic illustrations to help the readers and users to visualize the ideas and understand the abstract concepts. We also provided an introductory chapter where the main concepts and techniques needed to understand the offered materials of differential geometry are outlined to make the book fairly self-contained and reduce the need for external references.

Tensors Differential Forms And Variational Principles

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Author : David Lovelock
language : en
Publisher: Courier Corporation
Release Date : 2012-04-20

Tensors Differential Forms And Variational Principles written by David Lovelock and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-20 with Mathematics categories.

Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.