Concepts From Tensor Analysis And Differential Geometry By Tracy Y Thomas

Author : Tracy Y. Thomas
Publisher : Elsevier
Page : 128 pages
File Size : 54,7 Mb
Release : 2016-06-03
Category : Mathematics
ISBN : 9781483263717

Get Book

Concepts from Tensor Analysis and Differential Geometry by Tracy Y. Thomas Pdf

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.

Author : Tracy Yerkes Thomas
Publisher : Unknown
Page : 126 pages
File Size : 44,8 Mb
Release : 2013-08
Category : Electronic
ISBN : 1258786850

Get Book

Concepts from Tensor Analysis and Differential Geometry by Tracy Yerkes Thomas Pdf

Author : Anonim
Publisher : Elsevier
Page : 322 pages
File Size : 45,5 Mb
Release : 2000-04-01
Category : Mathematics
ISBN : 0080957781

Get Book

Concepts from Tensor Analysis and Differential Geometry by Tracy Y Thomas by Anonim Pdf

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

Author : Anonim
Publisher : Elsevier
Page : 322 pages
File Size : 44,7 Mb
Release : 1961-01-01
Category : Mathematics
ISBN : 0080955118

Get Book

Plastic Flow and Fracture in Solids by Tracy Y Thomas by Anonim Pdf

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

Author : Anonim
Publisher : Elsevier
Page : 322 pages
File Size : 55,9 Mb
Release : 2000-04-01
Category : Mathematics
ISBN : 0080955576

Get Book

Differential Geometry and the Calculus of Variations by Robert Hermann by Anonim Pdf

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

Author : Robert C. Wrede
Publisher : Courier Corporation
Page : 418 pages
File Size : 49,9 Mb
Release : 2013-01-30
Category : Mathematics
ISBN : 9780486137117

Get Book

Introduction to Vector and Tensor Analysis by Robert C. Wrede Pdf

Examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, and more. 1963 edition.

Author : Dipankar De
Publisher : John Wiley & Sons
Page : 516 pages
File Size : 50,8 Mb
Release : 2022-05-24
Category : Mathematics
ISBN : 9781119795629

Get Book

Introduction to Differential Geometry with Tensor Applications by Dipankar De Pdf

INTRODUCTION TO DIFFERENTIAL GEOMETRY WITH TENSOR APPLICATIONS This is the only volume of its kind to explain, in precise and easy-to-understand language, the fundamentals of tensors and their applications in differential geometry and analytical mechanics with examples for practical applications and questions for use in a course setting. Introduction to Differential Geometry with Tensor Applications discusses the theory of tensors, curves and surfaces and their applications in Newtonian mechanics. Since tensor analysis deals with entities and properties that are independent of the choice of reference frames, it forms an ideal tool for the study of differential geometry and also of classical and celestial mechanics. This book provides a profound introduction to the basic theory of differential geometry: curves and surfaces and analytical mechanics with tensor applications. The author has tried to keep the treatment of the advanced material as lucid and comprehensive as possible, mainly by including utmost detailed calculations, numerous illustrative examples, and a wealth of complementing exercises with complete solutions making the book easily accessible even to beginners in the field. Groundbreaking and thought-provoking, this volume is an outstanding primer for modern differential geometry and is a basic source for a profound introductory course or as a valuable reference. It can even be used for self-study, by students or by practicing engineers interested in the subject. Whether for the student or the veteran engineer or scientist, Introduction to Differential Geometry with Tensor Applications is a must-have for any library. This outstanding new volume: Presents a unique perspective on the theories in the field not available anywhere else Explains the basic concepts of tensors and matrices and their applications in differential geometry and analytical mechanics Is filled with hundreds of examples and unworked problems, useful not just for the student, but also for the engineer in the field Is a valuable reference for the professional engineer or a textbook for the engineering student

Author : Emil de Souza Sánchez Filho
Publisher : Springer
Page : 345 pages
File Size : 53,5 Mb
Release : 2016-05-20
Category : Technology & Engineering
ISBN : 9783319315201

Get Book

Tensor Calculus for Engineers and Physicists by Emil de Souza Sánchez Filho Pdf

This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of n-dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without needing to resort to other bibliographical sources on tensors. Chapter 1 deals with Fundamental Concepts about tensors and chapter 2 is devoted to the study of covariant, absolute and contravariant derivatives. The chapters 3 and 4 are dedicated to the Integral Theorems and Differential Operators, respectively. Chapter 5 deals with Riemann Spaces, and finally the chapter 6 presents a concise study of the Parallelism of Vectors. It also shows how to solve various problems of several particular manifolds.

Author : Hermes
Publisher : Academic Press
Page : 135 pages
File Size : 45,9 Mb
Release : 1969
Category : Computers
ISBN : 9780080955650

Get Book

Functional Analysis and Time Optimal Control by Hermes Pdf

Functional Analysis and Time Optimal Control

Author : Anonim
Publisher : Elsevier
Page : 322 pages
File Size : 45,5 Mb
Release : 1966-01-01
Category : Mathematics
ISBN : 0080955363

Get Book

Algebraic Linguistics; Analytical Models by Solomon Marcus by Anonim Pdf

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

Author : Urabe
Publisher : Academic Press
Page : 329 pages
File Size : 44,6 Mb
Release : 1967-01-01
Category : Computers
ISBN : 008095541X

Get Book

Nonlinear Autonomous Oscillations: Analytical Theory by Urabe Pdf

Nonlinear Autonomous Oscillations presents a self-contained and readable account for mathematicians, physicists, and engineers. This monograph is mainly concerned with the analytical theory of nonlinear autonomous oscillations, with the approach based mostly on the author’s work. After some introductory material, in Chapter 5 a moving orthogonal coordinate system along a closed orbit is introduced. In the next four chapters, stability theory and perturbation theory are systematically discussed for general autonomous systems by means of a moving coordinate system. In Chapter 10, the two-dimensional autonomous system is discussed in detail on the basis of results obtained in the preceding chapters. In Chapter 11, a numerical method for determining a periodic solution of the general nonlinear autonomous system is described. To illustrate this, the periodic solutions of the autonomous van der Pol equation for various values of the damping coefficient are computed. Chapter 12, which is based on the work of the author and Sibuya, discusses the center of higher dimension. Chapter 13 discusses a particular inverse problem connected with the period of periodic solutions of one interesting equation. There are, of course, many other topics of importance in the theory of nonlinear autonomous oscillations. These are, however, omitted in the present monograph because they are mainly topological rather than analytical and in order to keep the book from growing inordinately long.

Author : V. Lakshmikantham,S. Leela
Publisher : Academic Press
Page : 389 pages
File Size : 51,8 Mb
Release : 1969
Category : Computers
ISBN : 9780080955636

Get Book

Differential and Integral Inequalities: Theory and Applications by V. Lakshmikantham,S. Leela Pdf

This volume constitutes the first part of a monograph on theory and applications of differential and integral inequalities. 'The entire work, as a whole, is intended to be a research monograph, a guide to the literature, and a textbook for advanced courses. The unifying theme of this treatment is a systematic development of the theory and applications of differential inequalities as well as Volterra integral inequalities. The main tools for applications are the norm and the Lyapunov functions. Familiarity with real and complex analysis, elements of general topology and functional analysis, and differential and integral equations is assumed.

Author : Gilbert
Publisher : Academic Press
Page : 310 pages
File Size : 48,8 Mb
Release : 1969
Category : Computers
ISBN : 9780080955629

Get Book

Function Theoretic Methods in Partial Differential Equations by Gilbert Pdf

Function Theoretic Methods in Partial Differential Equations

Author : W. F. Ames
Publisher : Academic Press
Page : 282 pages
File Size : 44,7 Mb
Release : 1968
Category : Computers
ISBN : 9780080955506

Get Book

Nonlinear Ordinary Differential Equations in Transport Processes by W. F. Ames Pdf

Nonlinear Ordinary Differential Equations in Transport Processes

Author : C. A. Swanson
Publisher : Elsevier
Page : 238 pages
File Size : 44,8 Mb
Release : 2016-06-03
Category : Mathematics
ISBN : 9781483266671

Get Book

Comparison and Oscillation Theory of Linear Differential Equations by C. A. Swanson Pdf

Mathematics in Science and Engineering, Volume 48: Comparison and Oscillation Theory of Linear Differential Equations deals primarily with the zeros of solutions of linear differential equations. This volume contains five chapters. Chapter 1 focuses on comparison theorems for second order equations, while Chapter 2 treats oscillation and nonoscillation theorems for second order equations. Separation, comparison, and oscillation theorems for fourth order equations are covered in Chapter 3. In Chapter 4, ordinary equations and systems of differential equations are reviewed. The last chapter discusses the result of the first analog of a Sturm-type comparison theorem for an elliptic partial differential equation. This publication is intended for college seniors or beginning graduate students who are well-acquainted with advanced calculus, complex analysis, linear algebra, and linear differential equations.