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Differential Forms and Connections

Differential Forms and Connections
  • Author : R. W. R. Darling
  • Publisher :Unknown
  • Release Date :1994-09-22
  • Total pages :256
  • ISBN : 0521468000
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Summary : 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

Differential Forms
  • Author : Henri Cartan
  • Publisher :Unknown
  • Release Date :2012-07-06
  • Total pages :176
  • ISBN : 9780486139111
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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.

Differential Forms with Applications to the Physical Sciences

Differential Forms with Applications to the Physical Sciences
  • Author : Harley Flanders
  • Publisher :Unknown
  • Release Date :2012-04-26
  • Total pages :240
  • ISBN : 9780486139616
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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 Applications

Differential Forms and Applications
  • Author : Manfredo P. Do Carmo
  • Publisher :Unknown
  • Release Date :2012-12-06
  • Total pages :118
  • ISBN : 9783642579516
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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.

Tensors, Differential Forms, and Variational Principles

Tensors, Differential Forms, and Variational Principles
  • Author : David Lovelock,Hanno Rund
  • Publisher :Unknown
  • Release Date :2012-04-20
  • Total pages :400
  • ISBN : 9780486131986
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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.

A Geometric Approach to Differential Forms

A Geometric Approach to Differential Forms
  • Author : David Bachman
  • Publisher :Unknown
  • Release Date :2012-02-02
  • Total pages :156
  • ISBN : 9780817683047
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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.

Geometry of Differential Forms

Geometry of Differential Forms
  • Author : Shigeyuki Morita
  • Publisher :Unknown
  • Release Date :2001
  • Total pages :321
  • ISBN : 0821810456
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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.

Differential Forms on Singular Varieties

Differential Forms on Singular Varieties
  • Author : Vincenzo Ancona,Bernard Gaveau
  • Publisher :Unknown
  • Release Date :2005-08-24
  • Total pages :312
  • ISBN : 1420026526
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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

Differential Forms

Differential Forms
  • Author : Guillemin Victor,Haine Peter
  • Publisher :Unknown
  • Release Date :2019-03-20
  • Total pages :272
  • ISBN : 9789813272798
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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.

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 :Unknown
  • Release Date :2018-11-03
  • Total pages :468
  • ISBN : 9783319969923
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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 :Unknown
  • Release Date :1997
  • Total pages :256
  • ISBN : 0127425101
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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

Differential Forms
  • Author : M. Schreiber
  • Publisher :Unknown
  • Release Date :2012-12-06
  • Total pages :150
  • ISBN : 9781461299400
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Summary : A working knowledge of differential forms so strongly illuminates the calculus and its developments that it ought not be too long delayed in the curriculum. On the other hand, the systematic treatment of differential forms requires an apparatus of topology and algebra which is heavy for beginning undergraduates. Several texts on advanced calculus using differential forms have appeared in recent years. We may cite as representative of the variety of approaches the books of Fleming [2], (1) Nickerson-Spencer-Steenrod [3], and Spivak [6]. . Despite their accommodation to the innocence of their readers, these texts cannot lighten the burden of apparatus exactly because they offer a more or less full measure of the truth at some level of generality in a formally precise exposition. There. is consequently a gap between texts of this type and the traditional advanced calculus. Recently, on the occasion of offering a beginning course of advanced calculus, we undertook the expe- ment of attempting to present the technique of differential forms with minimal apparatus and very few prerequisites. These notes are the result of that experiment. Our exposition is intended to be heuristic and concrete. Roughly speaking, we take a differential form to be a multi-dimensional integrand, such a thing being subject to rules making change-of-variable calculations automatic. The domains of integration (manifolds) are explicitly given "surfaces" in Euclidean space. The differentiation of forms (exterior (1) Numbers in brackets refer to the Bibliography at the end.

Advanced Calculus

Advanced Calculus
  • Author : Harold M. Edwards
  • Publisher :Unknown
  • Release Date :1994-01-05
  • Total pages :508
  • ISBN : 0817637079
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Summary : 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.

Differential Forms

Differential Forms
  • Author : Steven H. Weintraub
  • Publisher :Unknown
  • Release Date :2014-02-19
  • Total pages :408
  • ISBN : 9780123946171
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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

Differential Forms in Algebraic Topology

Differential Forms in Algebraic Topology
  • Author : Raoul Bott,Loring W. Tu
  • Publisher :Unknown
  • Release Date :2013-04-17
  • Total pages :338
  • ISBN : 9781475739510
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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.

Inequalities for Differential Forms

Inequalities for Differential Forms
  • Author : Ravi P. Agarwal,Shusen Ding,Craig Nolder
  • Publisher :Unknown
  • Release Date :2009-09-19
  • Total pages :387
  • ISBN : 9780387684178
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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 in Mathematical Physics

Differential Forms in Mathematical Physics
  • Author : Anonim
  • Publisher :Unknown
  • Release Date :2009-06-17
  • Total pages :484
  • ISBN : 0080875246
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Summary : Differential Forms in Mathematical Physics

Exterior Analysis

Exterior Analysis
  • Author : Erdogan Suhubi
  • Publisher :Unknown
  • Release Date :2013-09-13
  • Total pages :779
  • ISBN : 9780124159280
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Summary : 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

Differential Forms on Regular Affine Algebra

Differential Forms on Regular Affine Algebra
  • Author : Gerhard Paul Hochschild,Alex Rosenberg,Bertram Kostant
  • Publisher :Unknown
  • Release Date :1961
  • Total pages :92
  • ISBN : UOM:39015095248566
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Summary : A mathematical discussion of the algebras of differential forms is treated as a special combination of linear algebra and homological alegbra. There is specific identification of this particular exterior algebra as applied to canical graded algebra based on the Tor functor and obtained by the cohomology of differential forms from the ext functor to a universal algebra i. e. Lie algebra. Attention is directed chiefly to a regular affine algebra, K-algebra, which is Noetherian with a finite Krull dimension, i. e. the largest non-negative integer.

Differential Forms in Electromagnetics

Differential Forms in Electromagnetics
  • Author : Ismo V. Lindell
  • Publisher :Unknown
  • Release Date :2004-04-27
  • Total pages :253
  • ISBN : 0471648019
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Summary : An introduction to multivectors, dyadics, and differential forms for electrical engineers While physicists have long applied differential forms to various areas of theoretical analysis, dyadic algebra is also the most natural language for expressing electromagnetic phenomena mathematically. George Deschamps pioneered the application of differential forms to electrical engineering but never completed his work. Now, Ismo V. Lindell, an internationally recognized authority on differential forms, provides a clear and practical introduction to replacing classical Gibbsian vector calculus with the mathematical formalism of differential forms. In Differential Forms in Electromagnetics, Lindell simplifies the notation and adds memory aids in order to ease the reader's leap from Gibbsian analysis to differential forms, and provides the algebraic tools corresponding to the dyadics of Gibbsian analysis that have long been missing from the formalism. He introduces the reader to basic EM theory and wave equations for the electromagnetic two-forms, discusses the derivation of useful identities, and explains novel ways of treating problems in general linear (bi-anisotropic) media. Clearly written and devoid of unnecessary mathematical jargon, Differential Forms in Electromagnetics helps engineers master an area of intense interest for anyone involved in research on metamaterials.

Regular Differential Forms

Regular Differential Forms
  • Author : Ernst Kunz,Rolf Waldi
  • Publisher :Unknown
  • Release Date :1988
  • Total pages :153
  • ISBN : 9780821850855
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Summary : This book is aimed at students and researchers in commutative algebra, algebraic geometry, and neighboring disciplines. The book will provide readers with new insight into differential forms and may stimulate new research through the many open questions it raises. The authors introduce various sheaves of differential forms for equidimensional morphisms of finite type between noetherian schemes, the most important being the sheaf of regular differential forms. It is known in many cases that the top degree regular differentials form a dualizing sheaf in the sense of duality theory. All constructions in the book are purely local and require only prerequisites from the theory of commutative noetherian rings and their Kahler differentials. The authors study the relations between the sheaves under consideration and give some applications to local properties of morphisms.The investigation of the 'fundamental class', a canonical homomorphism from Kahler to regular differential forms, is a major topic. The book closes with applications to curve singularities. While regular differential forms have been previously studied mainly in the 'absolute case' (that is, for algebraic varieties over fields), this book deals with the relative situation. Moreover, the authors strive to avoid 'separability assumptions'. Once the construction of regular differential forms is given, many results can be transferred from the absolute to the relative case.