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Author: Paul Renteln
Publisher: Cambridge University Press
ISBN: 1107042194
Category : Mathematics
Languages : en
Pages : 343
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Book Description
Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences.
Author: Paul Renteln
Publisher: Cambridge University Press
ISBN: 1107042194
Category : Mathematics
Languages : en
Pages : 343
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Book Description
Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences.
Author: Richard L. Bishop
Publisher: Courier Corporation
ISBN: 0486139239
Category : Mathematics
Languages : en
Pages : 290
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Book Description
DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div
Author: Robert Wasserman
Publisher: Oxford University Press, USA
ISBN: 9780198510598
Category : Language Arts & Disciplines
Languages : en
Pages : 468
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Book Description
This book sets forth the basic principles of tensors and manifolds and describes how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics.
Author: Ralph Abraham
Publisher: Springer Science & Business Media
ISBN: 1461210291
Category : Mathematics
Languages : en
Pages : 666
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Book Description
The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development. Throughout the text supplementary topics are given, marked with the symbols ~ and {l:;J. This device enables the reader to skip various topics without disturbing the main flow of the text. Some of these provide additional background material intended for completeness, to minimize the necessity of consulting too many outside references. We treat finite and infinite-dimensional manifolds simultaneously. This is partly for efficiency of exposition. Without advanced applications, using manifolds of mappings, the study of infinite-dimensional manifolds can be hard to motivate.
Author: Robert Wasserman
Publisher: Oxford University Press, USA
ISBN: 9780195065619
Category : Science
Languages : en
Pages : 409
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Book Description
This book is based on courses taken by advanced undergraduate and beginning graduate students in mathematics and physics at Michigan State University. The courses were intended to present an introduction to the expanse of modern mathematics and its applications in modern mathematics and its application in modern physics. This book gives an introduction perspective to young students intending to go into a field of pure mathematics, and who, with the usual 'pigeon-hold' graduate curriculum, will not get an overall perspective for several years, much less any idea of application.
Author: Anadi Jiban Das
Publisher: Springer Science & Business Media
ISBN: 0387694692
Category : Science
Languages : en
Pages : 300
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Book Description
Here is a modern introduction to the theory of tensor algebra and tensor analysis. It discusses tensor algebra and introduces differential manifold. Coverage also details tensor analysis, differential forms, connection forms, and curvature tensor. In addition, the book investigates Riemannian and pseudo-Riemannian manifolds in great detail. Throughout, examples and problems are furnished from the theory of relativity and continuum mechanics.
Author: David Lovelock
Publisher: Courier Corporation
ISBN: 048613198X
Category : Mathematics
Languages : en
Pages : 402
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Book Description
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.
Author: Tracy Y. Thomas
Publisher: Elsevier
ISBN: 1483263711
Category : Mathematics
Languages : en
Pages : 128
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Book Description
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: Robert Wasserman
Publisher: Oxford University Press, USA
ISBN: 0198510594
Category : Language Arts & Disciplines
Languages : en
Pages : 464
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Book Description
This book sets forth the basic principles of tensors and manifolds and describes how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics.
Author: K.K. Dube
Publisher: I. K. International Pvt Ltd
ISBN: 9380026587
Category : Mathematics
Languages : en
Pages : 377
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Book Description
The purpose of this book is to give a simple, lucid, rigorous and comprehensive account of fundamental notions of Differential Geometry and Tensors. The book is self-contained and divided in two parts. Section A deals with Differential Geometry and Section B is devoted to the study of Tensors. Section A deals with: " Theory of curves, envelopes and developables. " Curves on surfaces and fundamental magnitudes, curvature of surfaces and lines of curvature. " Fundamental equations of surface theory. " Geodesics. Section B deals with: " Tensor algebra. " Tensor calculus. " Christoffel symbols and their properties. " Riemann symbols and Einstein space, and their properties. " Physical components of contravariant and covariant vectors. " Geodesics and Parallelism of vectors. " Differentiable manifolds, charts, atlases.
