Differential Forms With Applications To The Physical Sciences

Author : Harley Flanders
Publisher : Courier Corporation
Page : 226 pages
File Size : 40,9 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.

Author : Anonim
Publisher : Elsevier
Page : 322 pages
File Size : 55,6 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

Author : Harry Flanders
Publisher : Unknown
Page : 0 pages
File Size : 51,7 Mb
Release : 1963
Category : Differential forms
ISBN : OCLC:17519588

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Differential Forms by Harry Flanders Pdf

Author : Manfredo P. Do Carmo
Publisher : Springer Science & Business Media
Page : 124 pages
File Size : 46,8 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.

Author : Anonim
Publisher : Elsevier
Page : 484 pages
File Size : 54,9 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

Author : David Lovelock,Hanno Rund
Publisher : Courier Corporation
Page : 400 pages
File Size : 50,8 Mb
Release : 2012-04-20
Category : Mathematics
ISBN : 9780486131986

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Tensors, Differential Forms, and Variational Principles by David Lovelock,Hanno Rund Pdf

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 : Tevian Dray
Publisher : CRC Press
Page : 324 pages
File Size : 53,8 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.

Author : R. W. R. Darling
Publisher : Cambridge University Press
Page : 288 pages
File Size : 42,8 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.

Author : Harold M. Edwards
Publisher : Springer Science & Business Media
Page : 523 pages
File Size : 41,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461202714

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Advanced Calculus by Harold M. Edwards Pdf

This book is a high-level introduction to vector calculus based solidly on differential forms. Informal but sophisticated, it is geometrically and physically intuitive yet mathematically rigorous. It offers remarkably diverse applications, physical and mathematical, and provides a firm foundation for further studies.

Author : A. I. Borisenko,I. E. Tarapov
Publisher : Courier Corporation
Page : 288 pages
File Size : 55,9 Mb
Release : 2012-08-28
Category : Mathematics
ISBN : 9780486131900

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Vector and Tensor Analysis with Applications by A. I. Borisenko,I. E. Tarapov Pdf

Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.

Author : Ilka Agricola,Thomas Friedrich
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 45,8 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.

Author : Bernard F. Schutz
Publisher : Cambridge University Press
Page : 272 pages
File Size : 52,8 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.

Author : Bo-Yu Hou,Bo-Yuan Hou
Publisher : World Scientific Publishing Company
Page : 560 pages
File Size : 41,5 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.

Author : Erdogan Suhubi
Publisher : Elsevier
Page : 780 pages
File Size : 49,8 Mb
Release : 2013-09-13
Category : Technology & Engineering
ISBN : 9780124159280

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Exterior Analysis by Erdogan Suhubi Pdf

Exterior analysis uses differential forms (a mathematical technique) to analyze curves, surfaces, and structures. Exterior Analysis is a first-of-its-kind resource that uses applications of differential forms, offering a mathematical approach to solve problems in defining a precise measurement to ensure structural integrity. The book provides methods to study different types of equations and offers detailed explanations of fundamental theories and techniques to obtain concrete solutions to determine symmetry. It is a useful tool for structural, mechanical and electrical engineers, as well as physicists and mathematicians. Provides a thorough explanation of how to apply differential equations to solve real-world engineering problems Helps researchers in mathematics, science, and engineering develop skills needed to implement mathematical techniques in their research Includes physical applications and methods used to solve practical problems to determine symmetry

Author : Theodore Frankel
Publisher : Cambridge University Press
Page : 749 pages
File Size : 51,6 Mb
Release : 2011-11-03
Category : Mathematics
ISBN : 9781139505611

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The Geometry of Physics by Theodore Frankel Pdf

This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, the Dirac operator and spinors, and gauge fields, including Yang–Mills, the Aharonov–Bohm effect, Berry phase and instanton winding numbers, quarks and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. The book is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. This third edition includes an overview of Cartan's exterior differential forms, which previews many of the geometric concepts developed in the text.