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Author : E. C. Thompson
Publisher : Unknown
Page : 108 pages
File Size : 54,7 Mb
Release : 1979
Category : Tensor products
ISBN : UOM:39015015600672
Author : Anthony G. Williams
Publisher : Cambridge University Press
Page : 793 pages
File Size : 51,5 Mb
Release : 2022-08-04
Category : Science
ISBN : 9781108470902
This textbook offers a detailed and self-contained presentation of quantum field theory, suitable for advanced undergraduate and graduate level courses. The author provides full derivations wherever possible and adopts a pedagogical tone without sacrificing rigour. A fully worked solutions manual is available online for instructors.
Author : R. W. R. Darling
Publisher : Cambridge University Press
Page : 288 pages
File Size : 48,7 Mb
Release : 1994-09-22
Category : Mathematics
ISBN : 0521468000
Introducing the tools of modern differential geometry--exterior calculus, manifolds, vector bundles, connections--this textbook covers both classical surface theory, the modern theory of connections, and curvature. With no knowledge of topology assumed, the only prerequisites are multivariate calculus and linear algebra.
Author : Sergei Winitzki
Publisher : Sergei Winitzki
Page : 286 pages
File Size : 53,6 Mb
Release : 2009-07-30
Category : Science
ISBN : 9781409294962
This is a pedagogical introduction to the coordinate-free approach in basic finite-dimensional linear algebra. The reader should be already exposed to the array-based formalism of vector and matrix calculations. This book makes extensive use of the exterior (anti-commutative, "wedge") product of vectors. The coordinate-free formalism and the exterior product, while somewhat more abstract, provide a deeper understanding of the classical results in linear algebra. Without cumbersome matrix calculations, this text derives the standard properties of determinants, the Pythagorean formula for multidimensional volumes, the formulas of Jacobi and Liouville, the Cayley-Hamilton theorem, the Jordan canonical form, the properties of Pfaffians, as well as some generalizations of these results.
Author : Anthony Francis Ruston
Publisher : Cambridge University Press
Page : 314 pages
File Size : 43,6 Mb
Release : 2004-06-03
Category : Mathematics
ISBN : 0521604931
Presents analogues for operators on Banach spaces of Fredholm's solution of integral equations of the second kind.
Author : Patrick Iglesias-Zemmour
Publisher : American Mathematical Soc.
Page : 467 pages
File Size : 47,6 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9780821891315
Diffeology is an extension of differential geometry. With a minimal set of axioms, diffeology allows us to deal simply but rigorously with objects which do not fall within the usual field of differential geometry: quotients of manifolds (even non-Hausdorff), spaces of functions, groups of diffeomorphisms, etc. The category of diffeology objects is stable under standard set-theoretic operations, such as quotients, products, co-products, subsets, limits, and co-limits. With its right balance between rigor and simplicity, diffeology can be a good framework for many problems that appear in various areas of physics. Actually, the book lays the foundations of the main fields of differential geometry used in theoretical physics: differentiability, Cartan differential calculus, homology and cohomology, diffeological groups, fiber bundles, and connections. The book ends with an open program on symplectic diffeology, a rich field of application of the theory. Many exercises with solutions make this book appropriate for learning the subject.
Author : Takeo Yokonuma
Publisher : Unknown
Page : 128 pages
File Size : 52,5 Mb
Release : 1992
Category : Multilinear algebra
ISBN : 1470445190
This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. To facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including th.
Author : Katsumi Nomizu
Publisher : Unknown
Page : 190 pages
File Size : 55,6 Mb
Release : 1961
Category : Calculus of tensors
ISBN : STANFORD:36105031175644
Author : Manousos Markoutsakis
Publisher : CRC Press
Page : 702 pages
File Size : 44,5 Mb
Release : 2021-12-29
Category : Science
ISBN : 9781000530261
This book provides advanced undergraduate physics and mathematics students with an accessible yet detailed understanding of the fundamentals of differential geometry and symmetries in classical physics. Readers, working through the book, will obtain a thorough understanding of symmetry principles and their application in mechanics, field theory, and general relativity, and in addition acquire the necessary calculational skills to tackle more sophisticated questions in theoretical physics. Most of the topics covered in this book have previously only been scattered across many different sources of literature, therefore this is the first book to coherently present this treatment of topics in one comprehensive volume. Key features: Contains a modern, streamlined presentation of classical topics, which are normally taught separately Includes several advanced topics, such as the Belinfante energy-momentum tensor, the Weyl-Schouten theorem, the derivation of Noether currents for diffeomorphisms, and the definition of conserved integrals in general relativity Focuses on the clear presentation of the mathematical notions and calculational technique
Author : Huayi Chen,Atsushi Moriwaki
Publisher : Springer Nature
Page : 452 pages
File Size : 53,8 Mb
Release : 2020-01-29
Category : Mathematics
ISBN : 9789811517280
The purpose of this book is to build the fundament of an Arakelov theory over adelic curves in order to provide a unified framework for research on arithmetic geometry in several directions. By adelic curve is meant a field equipped with a family of absolute values parametrized by a measure space, such that the logarithmic absolute value of each non-zero element of the field is an integrable function on the measure space. In the literature, such construction has been discussed in various settings which are apparently transversal to each other. The authors first formalize the notion of adelic curves and discuss in a systematic way its algebraic covers, which are important in the study of height theory of algebraic points beyond Weil–Lang’s height theory. They then establish a theory of adelic vector bundles on adelic curves, which considerably generalizes the classic geometry of vector bundles or that of Hermitian vector bundles over an arithmetic curve. They focus on an analogue of the slope theory in the setting of adelic curves and in particular estimate the minimal slope of tensor product adelic vector bundles. Finally, by using the adelic vector bundles as a tool, a birational Arakelov geometry for projective variety over an adelic curve is developed. As an application, a vast generalization of Nakai–Moishezon’s criterion of positivity is proven in clarifying the arguments of geometric nature from several fundamental results in the classic geometry of numbers. Assuming basic knowledge of algebraic geometry and algebraic number theory, the book is almost self-contained. It is suitable for researchers in arithmetic geometry as well as graduate students focusing on these topics for their doctoral theses.
Author : Hongyu Guo
Publisher : World Scientific
Page : 246 pages
File Size : 40,8 Mb
Release : 2021-06-16
Category : Mathematics
ISBN : 9789811241031
Tensors have numerous applications in physics and engineering. There is often a fuzzy haze surrounding the concept of tensor that puzzles many students. The old-fashioned definition is difficult to understand because it is not rigorous; the modern definitions are difficult to understand because they are rigorous but at a cost of being more abstract and less intuitive.The goal of this book is to elucidate the concepts in an intuitive way but without loss of rigor, to help students gain deeper understanding. As a result, they will not need to recite those definitions in a parrot-like manner any more. This volume answers common questions and corrects many misconceptions about tensors. A large number of illuminating illustrations helps the reader to understand the concepts more easily.This unique reference text will benefit researchers, professionals, academics, graduate students and undergraduate students.
Author : Barden Dennis,Thomas Charles B
Publisher : World Scientific
Page : 232 pages
File Size : 49,8 Mb
Release : 2003-03-12
Category : Mathematics
ISBN : 9781911298236
This invaluable book, based on the many years of teaching experience of both authors, introduces the reader to the basic ideas in differential topology. Among the topics covered are smooth manifolds and maps, the structure of the tangent bundle and its associates, the calculation of real cohomology groups using differential forms (de Rham theory), and applications such as the Poincaré-Hopf theorem relating the Euler number of a manifold and the index of a vector field. Each chapter contains exercises of varying difficulty for which solutions are provided. Special features include examples drawn from geometric manifolds in dimension 3 and Brieskorn varieties in dimensions 5 and 7, as well as detailed calculations for the cohomology groups of spheres and tori.
Author : Wolfgang Hackbusch
Publisher : Springer Science & Business Media
Page : 525 pages
File Size : 47,7 Mb
Release : 2012-02-23
Category : Mathematics
ISBN : 9783642280276
Special numerical techniques are already needed to deal with nxn matrices for large n.Tensor data are of size nxnx...xn=n^d, where n^d exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. The monograph describes the methods how tensors can be practically treated and how numerical operations can be performed. Applications are problems from quantum chemistry, approximation of multivariate functions, solution of pde, e.g., with stochastic coefficients, etc.
Author : Ray M. Bowen,Chao-cheng Wang
Publisher : Springer
Page : 224 pages
File Size : 41,9 Mb
Release : 1976-05-31
Category : Mathematics
ISBN : UOM:39015017127955
To Volume 1 This work represents our effort to present the basic concepts of vector and tensor analysis. Volume 1 begins with a brief discussion of algebraic structures followed by a rather detailed discussion of the algebra of vectors and tensors. Volume 2 begins with a discussion of Euclidean manifolds, which leads to a development of the analytical and geometrical aspects of vector and tensor fields. We have not included a discussion of general differentiable manifolds. However, we have included a chapter on vector and tensor fields defined on hypersurfaces in a Euclidean manifold. In preparing this two-volume work, our intention was to present to engineering and science students a modern introduction to vectors and tensors. Traditional courses on applied mathematics have emphasized problem-solving techniques rather than the systematic development of concepts. As a result, it is possible for such courses to become terminal mathematics courses rather than courses which equip the student to develop his or her understanding further.
Author : Frederic Zolla,Gilles Renversez,Andre Nicolet,Boris Kuhlmey,Sebastien R L Guenneau,Didier Felbacq
Publisher : World Scientific
Page : 377 pages
File Size : 52,8 Mb
Release : 2005-01-19
Category : Science
ISBN : 9781783260454
This book aims to provide expert guidance to researchers experienced in classical technology, as well as to those new to the field. A variety of perspectives on Photonic Crystal Fibres (PCFs) is presented together with a thorough treatment of the theoretical, physical and mathematical foundations of the optics of PCFs. The range of expertise of the authors is reflected in the depth of coverage, which will benefit those approaching the subject for a variety of reasons and from diverse backgrounds. The study of PCFs enables us to understand how best to optimize their applications in communication or sensing, as devices confining light via new mechanisms (such as photonic bandgap effects). It also assists us in understanding them as physically important structures which require a sophisticated mathematical analysis when considering questions related to the definition of effective refractive index, and the link between large finite systems and infinite periodic systems. This book offers access to essential information on foundation concepts of a dynamic and evolving subject. It is ideal for those who wish to explore further an emerging and important branch of optics and photonics./a