Differential Forms And Applications

Author : Manfredo P. Do Carmo
Publisher : Springer Science & Business Media
Page : 136 pages
File Size : 43,8 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.

Author : Manfredo P. Do Carmo
Publisher : Springer Science & Business Media
Page : 124 pages
File Size : 46,7 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 : Harley Flanders
Publisher : Courier Corporation
Page : 226 pages
File Size : 49,9 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 : Celso Melchiades Doria
Publisher : Springer Nature
Page : 362 pages
File Size : 54,6 Mb
Release : 2021-07-19
Category : Mathematics
ISBN : 9783030778347

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Differentiability in Banach Spaces, Differential Forms and Applications by Celso Melchiades Doria Pdf

This book is divided into two parts, the first one to study the theory of differentiable functions between Banach spaces and the second to study the differential form formalism and to address the Stokes' Theorem and its applications. Related to the first part, there is an introduction to the content of Linear Bounded Operators in Banach Spaces with classic examples of compact and Fredholm operators, this aiming to define the derivative of Fréchet and to give examples in Variational Calculus and to extend the results to Fredholm maps. The Inverse Function Theorem is explained in full details to help the reader to understand the proof details and its motivations. The inverse function theorem and applications make up this first part. The text contains an elementary approach to Vector Fields and Flows, including the Frobenius Theorem. The Differential Forms are introduced and applied to obtain the Stokes Theorem and to define De Rham cohomology groups. As an application, the final chapter contains an introduction to the Harmonic Functions and a geometric approach to Maxwell's equations of electromagnetism.

Author : Ravi P. Agarwal,Shusen Ding,Craig Nolder
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 43,9 Mb
Release : 2009-09-19
Category : Mathematics
ISBN : 9780387684178

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Inequalities for Differential Forms by Ravi P. Agarwal,Shusen Ding,Craig Nolder Pdf

This monograph is the first one to systematically present a series of local and global estimates and inequalities for differential forms, in particular the ones that satisfy the A-harmonic equations. The presentation focuses on the Hardy-Littlewood, Poincare, Cacciooli, imbedded and reverse Holder inequalities. Integral estimates for operators, such as homotopy operator, the Laplace-Beltrami operator, and the gradient operator are discussed next. Additionally, some related topics such as BMO inequalities, Lipschitz classes, Orlicz spaces and inequalities in Carnot groups are discussed in the concluding chapter. An abundance of bibliographical references and historical material supplement the text throughout. This rigorous presentation requires a familiarity with topics such as differential forms, topology and Sobolev space theory. It will serve as an invaluable reference for researchers, instructors and graduate students in analysis and partial differential equations and could be used as additional material for specific courses in these fields.

Author : David Bachman
Publisher : Springer Science & Business Media
Page : 156 pages
File Size : 54,6 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 : 48,7 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 : 48,5 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 : Erdogan Suhubi
Publisher : Elsevier
Page : 780 pages
File Size : 45,6 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 : Manfredo Perdigão do Carmo
Publisher : Unknown
Page : 0 pages
File Size : 54,5 Mb
Release : 2010
Category : Differential forms
ISBN : OCLC:1357633888

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Differential Forms and Applications by Manfredo Perdigão do Carmo Pdf

Author : Harold M. Edwards
Publisher : Springer Science & Business Media
Page : 523 pages
File Size : 40,6 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 : David Lovelock,Hanno Rund
Publisher : Courier Corporation
Page : 400 pages
File Size : 52,9 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 : Steven H. Weintraub
Publisher : Academic Press
Page : 50 pages
File Size : 55,5 Mb
Release : 1997
Category : Business & Economics
ISBN : 0127425101

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Differential Forms by Steven H. Weintraub Pdf

This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques. Geared towards students taking courses in multivariable calculus, this innovative book aims to make the subject more readily understandable. Differential forms unify and simplify the subject of multivariable calculus, and students who learn the subject as it is presented in this book should come away with a better conceptual understanding of it than those who learn using conventional methods. * Treats vector calculus using differential forms * Presents a very concrete introduction to differential forms * Develops Stokess theorem in an easily understandable way * Gives well-supported, carefully stated, and thoroughly explained definitions and theorems. * Provides glimpses of further topics to entice the interested student

Author : Tevian Dray
Publisher : CRC Press
Page : 324 pages
File Size : 41,7 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 : Yves Talpaert
Publisher : CRC Press
Page : 480 pages
File Size : 52,6 Mb
Release : 2000-09-12
Category : Mathematics
ISBN : 0824703855

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Differential Geometry with Applications to Mechanics and Physics by Yves Talpaert Pdf

An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential forms; Lie derivative and Lie algebra; n-form integration on n-manifold; Riemann geometry; and more. It includes 133 solved exercises.