Differential Forms

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Differential Forms

Differential Forms
  • Author : Guillemin Victor,Haine Peter
  • Publisher :
  • Release Date :2019-03-20
  • Total pages :272
  • ISBN : 9813272791
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Summary : There already exist a number of excellent graduate textbooks on the theory of differential forms as well as a handful of very good undergraduate textbooks on multivariable calculus in which this subject is briefly touched upon but not elaborated on enough.The goal of this textbook is to be readable and usable for undergraduates. It is entirely devoted to the subject of differential forms and explores a lot of its important ramifications.In particular, our book provides a detailed and lucid account of a fundamental result in the theory of differential forms which is, as a rule, not touched upon in undergraduate texts: the isomorphism between the Čech cohomology groups of a differential manifold and its de Rham cohomology groups.

Differential Forms with Applications to the Physical Sciences

Differential Forms with Applications to the Physical Sciences
  • Author : Harley Flanders
  • Publisher :
  • Release Date :2012-04-26
  • Total pages :240
  • ISBN : 0486139611
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Summary : A graduate-level text utilizing exterior differential forms in the analysis of a variety of mathematical problems in the physical and engineering sciences. Includes 45 illustrations. Index.

Differential Forms and Connections

Differential Forms and Connections
  • Author : R. W. R. Darling
  • Publisher :
  • Release Date :1994-09-22
  • Total pages :256
  • ISBN : 9780521468008
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Summary : This book introduces the tools of modern differential geometry--exterior calculus, manifolds, vector bundles, connections--and covers both classical surface theory, the modern theory of connections, and curvature. Also included is a chapter on applications to theoretical physics. The author uses the powerful and concise calculus of differential forms throughout. Through the use of numerous concrete examples, the author develops computational skills in the familiar Euclidean context before exposing the reader to the more abstract setting of manifolds. The only prerequisites are multivariate calculus and linear algebra; no knowledge of topology is assumed. Nearly 200 exercises make the book ideal for both classroom use and self-study for advanced undergraduate and beginning graduate students in mathematics, physics, and engineering.

Differential Forms and Applications

Differential Forms and Applications
  • Author : Manfredo P. Do Carmo
  • Publisher :
  • Release Date :2012-12-06
  • Total pages :118
  • ISBN : 3642579515
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Summary : 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

Differential Forms
  • Author : Henri Cartan
  • Publisher :
  • Release Date :2012-07-06
  • Total pages :176
  • ISBN : 0486139115
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Summary : The famous mathematician addresses both pure and applied branches of mathematics in a book equally essential as a text, reference, or a brilliant mathematical exercise. "Superb." — Mathematical Review. 1971 edition.

Geometry of Differential Forms

Geometry of Differential Forms
  • Author : Shigeyuki Morita
  • Publisher :
  • Release Date :2001
  • Total pages :321
  • ISBN : 9780821810453
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Summary : Since the times of Gauss, Riemann, and Poincare, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties. Among the high points on this route are the Gauss-Bonnet formula, the de Rham complex, and the Hodge theorem; these results show, in particular, that the central tool in reaching the main goal of global analysis is the theory of differential forms. This book is a comprehensive introduction to differential forms. It begins with a quick presentation of the notion of differentiable manifolds and then develops basic properties of differential forms as well as fundamental results about them, such as the de Rham and Frobenius theorems.The second half of the book is devoted to more advanced material, including Laplacians and harmonic forms on manifolds, the concepts of vector bundles and fiber bundles, and the theory of characteristic classes. Among the less traditional topics treated in the book is a detailed description of the Chern-Weil theory. With minimal prerequisites, the book can serve as a textbook for an advanced undergraduate or a graduate course in differential geometry.

A Visual Introduction to Differential Forms and Calculus on Manifolds

A Visual Introduction to Differential Forms and Calculus on Manifolds
  • Author : Jon Pierre Fortney
  • Publisher :
  • Release Date :2018-11-03
  • Total pages :468
  • ISBN : 3319969927
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Summary : 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.

Differential Forms

Differential Forms
  • Author : Steven H. Weintraub
  • Publisher :
  • Release Date :1997
  • Total pages :256
  • ISBN : 9780127425108
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Summary : 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

Differential Forms in Mathematical Physics

Differential Forms in Mathematical Physics
  • Author : N.A
  • Publisher :
  • Release Date :2009-06-17
  • Total pages :484
  • ISBN : 9780080875248
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Summary : Differential Forms in Mathematical Physics

Cohomology and Differential Forms

Cohomology and Differential Forms
  • Author : Izu Vaisman
  • Publisher :
  • Release Date :2016-07-28
  • Total pages :304
  • ISBN : 0486815129
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Summary : Self-contained development of cohomological theory of manifolds with various sheaves and its application to differential geometry covers categories and functions, sheaves and cohomology, fiber and vector bundles, and cohomology classes and differential forms. 1973 edition.

The Pullback Equation for Differential Forms

The Pullback Equation for Differential Forms
  • Author : Gyula Csató,Bernard Dacorogna,Olivier Kneuss
  • Publisher :
  • Release Date :2011-11-12
  • Total pages :436
  • ISBN : 0817683135
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Summary : An important question in geometry and analysis is to know when two k-forms f and g are equivalent through a change of variables. The problem is therefore to find a map φ so that it satisfies the pullback equation: φ*(g) = f. In more physical terms, the question under consideration can be seen as a problem of mass transportation. The problem has received considerable attention in the cases k = 2 and k = n, but much less when 3 ≤ k ≤ n–1. The present monograph provides the first comprehensive study of the equation. The work begins by recounting various properties of exterior forms and differential forms that prove useful throughout the book. From there it goes on to present the classical Hodge–Morrey decomposition and to give several versions of the Poincaré lemma. The core of the book discusses the case k = n, and then the case 1≤ k ≤ n–1 with special attention on the case k = 2, which is fundamental in symplectic geometry. Special emphasis is given to optimal regularity, global results and boundary data. The last part of the work discusses Hölder spaces in detail; all the results presented here are essentially classical, but cannot be found in a single book. This section may serve as a reference on Hölder spaces and therefore will be useful to mathematicians well beyond those who are only interested in the pullback equation. The Pullback Equation for Differential Forms is a self-contained and concise monograph intended for both geometers and analysts. The book may serve as a valuable reference for researchers or a supplemental text for graduate courses or seminars.

A Geometric Approach to Differential Forms

A Geometric Approach to Differential Forms
  • Author : David Bachman
  • Publisher :
  • Release Date :2012-02-02
  • Total pages :156
  • ISBN : 0817683046
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Summary : 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.

Differential Forms

Differential Forms
  • Author : Steven H. Weintraub
  • Publisher :
  • Release Date :2014-02-19
  • Total pages :408
  • ISBN : 0123946174
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Summary : Differential forms are a powerful mathematical technique to help students, researchers, and engineers solve problems in geometry and analysis, and their applications. They both unify and simplify results in concrete settings, and allow them to be clearly and effectively generalized to more abstract settings. Differential Forms has gained high recognition in the mathematical and scientific community as a powerful computational tool in solving research problems and simplifying very abstract problems. Differential Forms, 2nd Edition, is a solid resource for students and professionals needing a general understanding of the mathematical theory and to be able to apply that theory into practice. Provides a solid theoretical basis of how to develop and apply differential forms to real research problems Includes computational methods to enable the reader to effectively use differential forms Introduces theoretical concepts in an accessible manner

Invariants of Quadratic Differential Forms

Invariants of Quadratic Differential Forms
  • Author : N.A
  • Publisher :
  • Release Date :
  • Total pages :329
  • ISBN :
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Summary :

Inequalities for Differential Forms

Inequalities for Differential Forms
  • Author : Ravi P. Agarwal,Shusen Ding,Craig Nolder
  • Publisher :
  • Release Date :2009-09-19
  • Total pages :387
  • ISBN : 0387684174
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Summary : 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.

Differential Forms

Differential Forms
  • Author : Harley Flanders
  • Publisher :
  • Release Date :1963
  • Total pages :203
  • ISBN :
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Summary : Introduces the use of exterior differential forms as a powerful took in the analysis of a variety of mathematical problems in the physical and engineering sciences.

Differential Forms on Singular Varieties

Differential Forms on Singular Varieties
  • Author : Vincenzo Ancona,Bernard Gaveau
  • Publisher :
  • Release Date :2005-08-24
  • Total pages :312
  • ISBN : 9781420026528
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Summary : Differential Forms on Singular Varieties: De Rham and Hodge Theory Simplified uses complexes of differential forms to give a complete treatment of the Deligne theory of mixed Hodge structures on the cohomology of singular spaces. This book features an approach that employs recursive arguments on dimension and does not introduce spaces of hig

Tensors, Differential Forms, and Variational Principles

Tensors, Differential Forms, and Variational Principles
  • Author : David Lovelock,Hanno Rund
  • Publisher :
  • Release Date :2012-04-20
  • Total pages :400
  • ISBN : 048613198X
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Summary : 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.

Differential Forms in Algebraic Topology

Differential Forms in Algebraic Topology
  • Author : Raoul Bott,Loring W. Tu
  • Publisher :
  • Release Date :2013-04-17
  • Total pages :338
  • ISBN : 1475739516
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Summary : 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.

Invariants of Quadratic Differential Forms

Invariants of Quadratic Differential Forms
  • Author : J. Edmund Wright
  • Publisher :
  • Release Date :2015-03-26
  • Total pages :100
  • ISBN : 1107493935
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Summary : Originally published in 1908, this book provides a concise account regarding the invariant theory connected with a single quadratic differential form.