Differential Forms With Applications To The Physical Sciences

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Differential Forms with Applications to the Physical Sciences

Author : Harley Flanders
Publisher : Courier Corporation
Page : 226 pages
File Size : 53,8 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486139616

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Differential Forms with Applications to the Physical Sciences by Harley Flanders Pdf

"To the reader who wishes to obtain a bird's-eye view of the theory of differential forms with applications to other branches of pure mathematics, applied mathematic and physics, I can recommend no better book." — T. J. Willmore, London Mathematical Society Journal. This excellent text introduces the use of exterior differential forms as a powerful tool in the analysis of a variety of mathematical problems in the physical and engineering sciences. Requiring familiarity with several variable calculus and some knowledge of linear algebra and set theory, it is directed primarily to engineers and physical scientists, but it has also been used successfully to introduce modern differential geometry to students in mathematics. Chapter I introduces exterior differential forms and their comparisons with tensors. The next three chapters take up exterior algebra, the exterior derivative and their applications. Chapter V discusses manifolds and integration, and Chapter VI covers applications in Euclidean space. The last three chapters explore applications to differential equations, differential geometry, and group theory. "The book is very readable, indeed, enjoyable — and, although addressed to engineers and scientists, should be not at all inaccessible to or inappropriate for ... first year graduate students and bright undergraduates." — F. E. J. Linton, Wesleyan University, American Mathematical Monthly.

Differential Forms with Applications to the Physical Sciences by Harley Flanders

Author : Anonim
Publisher : Elsevier
Page : 322 pages
File Size : 53,5 Mb
Release : 1963-01-01
Category : Mathematics
ISBN : 0080955185

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Differential Forms with Applications to the Physical Sciences by Harley Flanders 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

Differential Forms

Author : Harry Flanders
Publisher : Unknown
Page : 0 pages
File Size : 41,5 Mb
Release : 1963
Category : Differential forms
ISBN : OCLC:17519588

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Differential Forms by Harry Flanders Pdf

Differential Forms and Applications

Author : Manfredo P. Do Carmo
Publisher : Springer Science & Business Media
Page : 136 pages
File Size : 46,9 Mb
Release : 1998-05-20
Category : Mathematics
ISBN : 3540576185

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Differential Forms and Applications by Manfredo P. Do Carmo Pdf

An application of differential forms for the study of some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to "users" of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem, namely Stokes' theorem, can be presented in its natural setting. The applications consist in developing the method of moving frames expounded by E. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces. This is then collated in the last chapter to present Chern's proof of the Gauss-Bonnet theorem for compact surfaces.

Differential Forms in Mathematical Physics

Author : Anonim
Publisher : Elsevier
Page : 484 pages
File Size : 52,8 Mb
Release : 2009-06-17
Category : Mathematics
ISBN : 0080875246

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Differential Forms in Mathematical Physics by Anonim Pdf

Differential Forms in Mathematical Physics

Differential Forms and Connections

Author : R. W. R. Darling
Publisher : Cambridge University Press
Page : 288 pages
File Size : 54,9 Mb
Release : 1994-09-22
Category : Mathematics
ISBN : 0521468000

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Differential Forms and Connections by R. W. R. Darling Pdf

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.

Differential Forms and Applications

Author : Manfredo P. Do Carmo
Publisher : Springer Science & Business Media
Page : 124 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642579516

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Differential Forms and Applications by Manfredo P. Do Carmo Pdf

An application of differential forms for the study of some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to "users" of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem, namely Stokes' theorem, can be presented in its natural setting. The applications consist in developing the method of moving frames expounded by E. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces. This is then collated in the last chapter to present Chern's proof of the Gauss-Bonnet theorem for compact surfaces.

Differential Forms in Mathematical Physics

Author : C. von Westenholtz
Publisher : Unknown
Page : 563 pages
File Size : 50,5 Mb
Release : 1986
Category : Electronic
ISBN : OCLC:641135454

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Differential Forms in Mathematical Physics by C. von Westenholtz Pdf

Differential Forms and the Geometry of General Relativity

Author : Tevian Dray
Publisher : CRC Press
Page : 324 pages
File Size : 44,9 Mb
Release : 2014-10-20
Category : Mathematics
ISBN : 9781466510005

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Differential Forms and the Geometry of General Relativity by Tevian Dray Pdf

Differential Forms and the Geometry of General Relativity provides readers with a coherent path to understanding relativity. Requiring little more than calculus and some linear algebra, it helps readers learn just enough differential geometry to grasp the basics of general relativity. The book contains two intertwined but distinct halves. Designed for advanced undergraduate or beginning graduate students in mathematics or physics, most of the text requires little more than familiarity with calculus and linear algebra. The first half presents an introduction to general relativity that describes some of the surprising implications of relativity without introducing more formalism than necessary. This nonstandard approach uses differential forms rather than tensor calculus and minimizes the use of "index gymnastics" as much as possible. The second half of the book takes a more detailed look at the mathematics of differential forms. It covers the theory behind the mathematics used in the first half by emphasizing a conceptual understanding instead of formal proofs. The book provides a language to describe curvature, the key geometric idea in general relativity.

Global Analysis

Author : Ilka Agricola,Thomas Friedrich
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 42,6 Mb
Release : 2002
Category : Differential forms
ISBN : 9780821829516

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Global Analysis by Ilka Agricola,Thomas Friedrich Pdf

The final third of the book applies the mathematical ideas to important areas of physics: Hamiltonian mechanics, statistical mechanics, and electrodynamics." "There are many classroom-tested exercises and examples with excellent figures throughout. The book is ideal as a text for a first course in differential geometry, suitable for advanced undergraduates or graduate students in mathematics or physics."--BOOK JACKET.

Differential Geometry for Physicists

Author : Bo-Yu Hou,Bo-Yuan Hou
Publisher : World Scientific Publishing Company
Page : 560 pages
File Size : 48,5 Mb
Release : 1997-10-31
Category : Mathematics
ISBN : 9789813105096

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Differential Geometry for Physicists by Bo-Yu Hou,Bo-Yuan Hou Pdf

This book is divided into fourteen chapters, with 18 appendices as introduction to prerequisite topological and algebraic knowledge, etc. The first seven chapters focus on local analysis. This part can be used as a fundamental textbook for graduate students of theoretical physics. Chapters 8–10 discuss geometry on fibre bundles, which facilitates further reference for researchers. The last four chapters deal with the Atiyah-Singer index theorem, its generalization and its application, quantum anomaly, cohomology field theory and noncommutative geometry, giving the reader a glimpse of the frontier of current research in theoretical physics.

Geometrical Methods of Mathematical Physics

Author : Bernard F. Schutz
Publisher : Cambridge University Press
Page : 272 pages
File Size : 44,5 Mb
Release : 1980-01-28
Category : Science
ISBN : 9781107268142

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Geometrical Methods of Mathematical Physics by Bernard F. Schutz Pdf

In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.

Differential Forms in Algebraic Topology

Author : Raoul Bott,Loring W. Tu
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 50,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475739510

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Differential Forms in Algebraic Topology by Raoul Bott,Loring W. Tu Pdf

Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.

Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics

Author : Steinar Johannesen
Publisher : CRC Press
Page : 400 pages
File Size : 45,6 Mb
Release : 2016-12-08
Category : Mathematics
ISBN : 9781315342627

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Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics by Steinar Johannesen Pdf

This book provides a systematic presentation of the mathematical foundation of modern physics with applications particularly within classical mechanics and the theory of relativity. Written to be self-contained, Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics provides complete and rigorous proofs of all the results presented within. Among the themes illustrated in the book are differentiable manifolds, differential forms, fiber bundles and differential geometry with non-trivial applications especially within the general theory of relativity. The emphasis is upon a systematic and logical construction of the mathematical foundations. It can be used as a textbook for a pure mathematics course in differential geometry, assuming the reader has a good understanding of basic analysis, linear algebra and point set topology. The book will also appeal to students of theoretical physics interested in the mathematical foundation of the theories.

Differential Geometry, Gauge Theories, and Gravity

Author : M. Göckeler,T. Schücker
Publisher : Cambridge University Press
Page : 248 pages
File Size : 48,5 Mb
Release : 1989-07-28
Category : Mathematics
ISBN : 0521378214

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Differential Geometry, Gauge Theories, and Gravity by M. Göckeler,T. Schücker Pdf

Cambridge University Press is committed to keeping scholarly work in print for as long as possible. A short print-run of this academic paperback has been produced using digital technology. This technology has enabled Cambridge to keep the book in print for specialists and students when traditional methods of reprinting would not have been feasible. While the new digital cover differs from the original, the text content is identical to that of previous printings.