A Geometric Approach To Differential Forms

Author : David Bachman
Publisher : Springer Science & Business Media
Page : 156 pages
File Size : 53,5 Mb
Release : 2012-02-02
Category : Mathematics
ISBN : 9780817683047

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A Geometric Approach to Differential Forms by David Bachman Pdf

This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.

Author : Jon Pierre Fortney
Publisher : Springer
Page : 468 pages
File Size : 44,9 Mb
Release : 2018-11-03
Category : Mathematics
ISBN : 9783319969923

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A Visual Introduction to Differential Forms and Calculus on Manifolds by Jon Pierre Fortney Pdf

This book explains and helps readers to develop geometric intuition as it relates to differential forms. It includes over 250 figures to aid understanding and enable readers to visualize the concepts being discussed. The author gradually builds up to the basic ideas and concepts so that definitions, when made, do not appear out of nowhere, and both the importance and role that theorems play is evident as or before they are presented. With a clear writing style and easy-to- understand motivations for each topic, this book is primarily aimed at second- or third-year undergraduate math and physics students with a basic knowledge of vector calculus and linear algebra.

Author : R. W. R. Darling
Publisher : Cambridge University Press
Page : 288 pages
File Size : 55,9 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.

Author : John Snygg
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 42,5 Mb
Release : 2011-12-09
Category : Mathematics
ISBN : 9780817682835

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A New Approach to Differential Geometry using Clifford's Geometric Algebra by John Snygg Pdf

Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space. Complete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.

Author : Harold M. Edwards
Publisher : Springer Science & Business Media
Page : 523 pages
File Size : 53,9 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 : Tristan Needham
Publisher : Princeton University Press
Page : 530 pages
File Size : 48,7 Mb
Release : 2021-07-13
Category : Mathematics
ISBN : 9780691203706

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Visual Differential Geometry and Forms by Tristan Needham Pdf

An inviting, intuitive, and visual exploration of differential geometry and forms Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book. Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.

Author : Manfredo P. Do Carmo
Publisher : Springer Science & Business Media
Page : 124 pages
File Size : 40,5 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 : Peter J. Vassiliou,Ian G. Lisle
Publisher : Cambridge University Press
Page : 242 pages
File Size : 55,6 Mb
Release : 2000-03-13
Category : Mathematics
ISBN : 0521775981

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Geometric Approaches to Differential Equations by Peter J. Vassiliou,Ian G. Lisle Pdf

A concise and accessible introduction to the wide range of topics in geometric approaches to differential equations.

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 : Raoul Bott,Loring W. Tu
Publisher : Springer Science & Business Media
Page : 338 pages
File Size : 46,5 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.

Author : John Snygg
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 46,7 Mb
Release : 2011-12-08
Category : Mathematics
ISBN : 9780817682828

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A New Approach to Differential Geometry using Clifford's Geometric Algebra by John Snygg Pdf

Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space. Complete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.

Author : Barrett O'Neill
Publisher : Academic Press
Page : 422 pages
File Size : 42,5 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483268118

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Elementary Differential Geometry by Barrett O'Neill Pdf

Elementary Differential Geometry focuses on the elementary account of the geometry of curves and surfaces. The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives, Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry. The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates, and integration and orientation. The text is a valuable reference for students interested in elementary differential geometry.

Author : Tevian Dray
Publisher : CRC Press
Page : 324 pages
File Size : 52,8 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 : David Lovelock,Hanno Rund
Publisher : Courier Corporation
Page : 400 pages
File Size : 55,5 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 : John Hamal Hubbard,Barbara Burke Hubbard
Publisher : Unknown
Page : 284 pages
File Size : 53,8 Mb
Release : 2009
Category : Algebras, Linear
ISBN : 097157667X

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Student Solution Manual to Accompany the 4th Edition of Vector Calculus, Linear Algebra, and Differential Forms, a Unified Approach by John Hamal Hubbard,Barbara Burke Hubbard Pdf