6 edition of Tensor calculus through differential geometry found in the catalog.
Bibliography: p. 166.
|Statement||[by] J. Abram.|
|LC Classifications||QA641 .A3|
|The Physical Object|
|Pagination||v, 170 p.|
|Number of Pages||170|
|LC Control Number||66001182|
Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in theory of plane and space curves and surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century. Tensor calculus: a concise course Barry Spain This book will prove to be a good introduction, both for the physicist who wishes to make applications and for the mathematician who prefers to have a short survey before taking up one of the more voluminous textbooks on differential geometry.
Plus, Tensor Calculus is really just a corollary to Differential Geometry. EDIT: I usually don't do DG, I typically stick to Algebraic Geometry (which are both structurally similar thanks to Grothendieck), so I can't recommend the best introductory book. The best for an intuitive introduction is the first two volumes of Spivak, A comprehensive introduction to Differential Geometry. The prerequsites are calculus, and linear algebra Look at Spivak's Little book calculus on Manifolds. In Volume 2 you don't have to read the classic Papers by Gauss and Riemann, although it's fun to do so.
-tensor=scalar=number 26 1 0-tensor=contravariant1-tensor=vector 27 0 1-tensor=covariant1-tensor=covector 27 0 2-tensor=covariant2-tensor = lineartransformation:V!V 28 2 0-tensor=contravariant2-tensor = lineartransformation:V!V 32 1 1-tensor=mixed2-tensor = lineartransformation:V!V andV!V 35 0 3-tensor File Size: KB. Introduction to Tensor Analysis and the Calculus of Moving Surfaces: Grinfeld, Pavel this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape /5(63).
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If calculus and linear algebra are central to the reader’s scientific endeavors, tensor calculus is indispensable. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to by: This book includes both tensor calculus and differential geometry in a single volume.
This book provides a conceptual exposition of the fundamental results in the theory of tensors. It also illustrates the applications of tensors to differential geometry, mechanics and relativity. The authors present a thorough development of TENSOR CALCULUS, from basic principals, such as ordinary three dimensional vector space.
Tensors are generalizations of vectors to any number of dimensions (vectors are type (1,0) tensors, diff. forms are type (0,1) tensors).Cited by: texts All Books All Texts latest This Just In Smithsonian Libraries FEDLINK (US) Genealogy Lincoln Collection.
National Emergency Tensor calculus through differential geometry by Abram, J. (John) Publication date Topics Calculus of tensors, Geometry, Differential, Riemann surfaces Publisher London, ButterworthsPages: Introductory concepts --The two-dimensional curved surface --Special results --Some Riemannian geometry --Differential geometry --Further differential geometry --Applications of tensor methods to the mechanics of continuous media --Applications of tensor methods to dynamics.
The intuition behind tensor calculus is that we can construct tensor fields smoothly varying from point to point. At every point of a manifold (or Euclidean space, if you prefer) we can conceptualize the vector space of velocities through that point.
Linear algebra forms the skeleton of tensor calculus and differential geometry. We recall a few basic deﬁnitions from linear algebra, which will play a pivotal role throughout this course.
Reminder A vector space V over the ﬁeld K (R or C) is a set of objects that can be added and multiplied by scalars, suchFile Size: 1MB. Differential Geometry Lecture Notes. This book covers the following topics: Smooth Manifolds, Plain curves, Submanifolds, Differentiable maps, immersions, submersions and embeddings, Basic results from Differential Topology, Tangent spaces and tensor calculus, Riemannian geometry.
Tensors have their applications to Riemannian Geometry, Mechanics, Elasticity, Theory of Relativity, Electromagnetic Theory and many other disciplines of Science and Engineering.
This book has been presented in such a clear and easy way that the students will have no difficulty in understanding Size: 1MB. KEY WORDS: Curve, Frenet frame, curvature, torsion, hypersurface, funda-mental forms, principal curvature, Gaussian curvature, Minkowski curvature, manifold, tensor eld, connection, geodesic curve SUMMARY: The aim of this textbook is to give an introduction to di er-ential geometry.
It is based on the lectures given by the author at E otv os. Primarily intended for the undergraduate and postgraduate students of mathematics, this textbook covers both geometry and tensor in a single volume.
This book aims to provide a conceptual exposition of the fundamental results in the theory of tensors. It also illustrates the applications of tensors to differential geometry, mechanics and s: 2. § Tensor decomposition 11 § P v.
NP and algebraic variants 17 § Algebraic Statistics and tensor networks 21 § Geometry and representation theory 24 Chapter 2.
Multilinear algebra 27 § Rust removal exercises 28 § Groups and representations 30 § Tensor products 32 § The rank and border rank of a tensor 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. “This book attempts to give careful attention to the advice of both Cartan and Weyl and to present a clear geometric picture along with an effective and elegant analytical technique.
it should be emphasized that this book deepens its readers’ understanding of vector calculus, differential geometry, and related subjects in applied /5(63). This package introduces definitions for tensor calculations in Riemannian Geometry. To begin a calculation the user must specify a Riemannian space by giving: a list of symbols (= coordinates), a symmetric matrix of functions of the coordinates (= metric tensor) and a list of simplification rules (optional).
The main routine in the package -- RGtensors[metric_, coordinates_] -- then computes. An Introduction to Differential Geometry with Use of the Tensor Calculus. By Prof. Luther Pfahler Eisenhart. (Princeton Mathematical Series, 3.) Pp. x + Cited by: Tensor Calculus 9: Integration with Differential Forms Integration with Differential Forms Examples Tensor Calculus 6: Differential Forms are Covectors - Duration: I really, really love Manifolds, Tensors, and Forms: An Introduction for Mathematicians and Physicists by Paul Renteln.
It is mathematical—sorry—but it gives the bare-bones definitions that are needed to do differential geometry.
So all of the ele. introduction to tensor calculus and continuum mechanics In Part One I have included introductory topics in tensors, differential geometry and relativity. Part Two presents basics from the areas of continuum mechanics (dynamics, elasticity, fluids, electricity, magnetism).
Manifolds Generally speaking, amanifoldis a space that with curvature and complicated topology that locallylooks like Rn. Examples: Rn itself. R is a line and R2 a plane. The n-sphere, Sn; that is, the locus of all points some ﬁxed distance from the origin in Rn+ 1.S is a circle and S2 sphere.
The n-torus Tn.T2 is the surface of a doughnut. A Riemann surface of genus Size: KB. algebra and geometry. The early chapters have many words and few equations.
The deﬁnition of a tensor comes only in Chap. 6—when the reader is ready for it. Part III of this book is devoted to the calculus of moving surfaces (CMS).
One of the central applications of tensor calculus is differential geometry, and there isFile Size: 1MB.Books shelved as differential-geometry: Differential Geometry of Curves and Surfaces by Manfredo P.
An Introduction to Differential Geometry - With the Use of Tensor Calculus (Paperback) by. Luther Pfahler Eisenhart (shelved 2 times as differential-geometry) Tensors, Differential Forms, and Variational Principles (Paperback) by.
Tensor Calculus Lecture Geodesic Curvature Preview MathTheBeautiful. Coordinate Systems and the Role of Tensor Calculus Differential Geometry.