Differential Forms

Differential Forms
Author: Henri Cartan
Publsiher: Courier Corporation
Total Pages: 176
Release: 2012-07-06
ISBN 10: 0486139115
ISBN 13: 9780486139111
Language: EN, FR, DE, ES & NL

Differential Forms Book Review:

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
Publsiher: Courier Corporation
Total Pages: 240
Release: 2012-04-26
ISBN 10: 0486139611
ISBN 13: 9780486139616
Language: EN, FR, DE, ES & NL

Differential Forms with Applications to the Physical Sciences Book Review:

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

Differential Forms
Author: M. Schreiber
Publsiher: Springer Science & Business Media
Total Pages: 150
Release: 2012-12-06
ISBN 10: 1461299403
ISBN 13: 9781461299400
Language: EN, FR, DE, ES & NL

Differential Forms Book Review:

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.

Differential Forms and Applications

Differential Forms and Applications
Author: Manfredo P. Do Carmo
Publsiher: Springer Science & Business Media
Total Pages: 118
Release: 2012-12-06
ISBN 10: 3642579515
ISBN 13: 9783642579516
Language: EN, FR, DE, ES & NL

Differential Forms and Applications Book Review:

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
Publsiher: Courier Corporation
Total Pages: 400
Release: 2012-04-20
ISBN 10: 048613198X
ISBN 13: 9780486131986
Language: EN, FR, DE, ES & NL

Tensors Differential Forms and Variational Principles Book Review:

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 and Connections

Differential Forms and Connections
Author: R. W. R. Darling
Publsiher: Cambridge University Press
Total Pages: 256
Release: 1994-09-22
ISBN 10: 9780521468008
ISBN 13: 0521468000
Language: EN, FR, DE, ES & NL

Differential Forms and Connections Book Review:

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.

A Geometric Approach to Differential Forms

A Geometric Approach to Differential Forms
Author: David Bachman
Publsiher: Springer Science & Business Media
Total Pages: 156
Release: 2012-02-02
ISBN 10: 0817683046
ISBN 13: 9780817683047
Language: EN, FR, DE, ES & NL

A Geometric Approach to Differential Forms Book Review:

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.

Cohomology and Differential Forms

Cohomology and Differential Forms
Author: Izu Vaisman
Publsiher: Courier Dover Publications
Total Pages: 304
Release: 2016-08-17
ISBN 10: 0486804836
ISBN 13: 9780486804835
Language: EN, FR, DE, ES & NL

Cohomology and Differential Forms Book Review:

This monograph explores the cohomological theory of manifolds with various sheaves and its application to differential geometry. Based on lectures given by author Izu Vaisman at Romania's University of Iasi, the treatment is suitable for advanced undergraduates and graduate students of mathematics as well as mathematical researchers in differential geometry, global analysis, and topology. A self-contained development of cohomological theory constitutes the central part of the book. Topics include categories and functors, the Čech cohomology with coefficients in sheaves, the theory of fiber bundles, and differentiable, foliated, and complex analytic manifolds. The final chapter covers the theorems of de Rham and Dolbeault-Serre and examines the theorem of Allendoerfer and Eells, with applications of these theorems to characteristic classes and the general theory of harmonic forms.

Differential Forms

Differential Forms
Author: Guillemin Victor,Haine Peter
Publsiher: World Scientific
Total Pages: 272
Release: 2019-03-20
ISBN 10: 9813272791
ISBN 13: 9789813272798
Language: EN, FR, DE, ES & NL

Differential Forms Book Review:

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 and the Geometry of General Relativity

Differential Forms and the Geometry of General Relativity
Author: Tevian Dray
Publsiher: CRC Press
Total Pages: 321
Release: 2014-10-20
ISBN 10: 1466510005
ISBN 13: 9781466510005
Language: EN, FR, DE, ES & NL

Differential Forms and the Geometry of General Relativity Book Review:

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.

A Visual Introduction to Differential Forms and Calculus on Manifolds

A Visual Introduction to Differential Forms and Calculus on Manifolds
Author: Jon Pierre Fortney
Publsiher: Springer
Total Pages: 468
Release: 2018-11-03
ISBN 10: 3319969927
ISBN 13: 9783319969923
Language: EN, FR, DE, ES & NL

A Visual Introduction to Differential Forms and Calculus on Manifolds Book Review:

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
Publsiher: Academic Press
Total Pages: 256
Release: 1997
ISBN 10: 9780127425108
ISBN 13: 0127425101
Language: EN, FR, DE, ES & NL

Differential Forms Book Review:

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

Global Analysis

Global Analysis
Author: Ilka Agricola,Thomas Friedrich
Publsiher: American Mathematical Soc.
Total Pages: 343
Release: 2002
ISBN 10: 0821829513
ISBN 13: 9780821829516
Language: EN, FR, DE, ES & NL

Global Analysis Book Review:

This book introduces the reader to the world of differential forms and their uses in geometry, analysis, and mathematical physics. It begins with a few basic topics, partly as review, then moves on to vector analysis on manifolds and the study of curves and surfaces in $3$-space. Lie groups and homogeneous spaces are discussed, providing the appropriate framework for introducing symmetry in both mathematical and physical contexts. 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.

Differential Forms in Algebraic Topology

Differential Forms in Algebraic Topology
Author: Raoul Bott,Loring W. Tu
Publsiher: Springer Science & Business Media
Total Pages: 338
Release: 2013-04-17
ISBN 10: 1475739516
ISBN 13: 9781475739510
Language: EN, FR, DE, ES & NL

Differential Forms in Algebraic Topology Book Review:

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.

Differential Forms

Differential Forms
Author: Steven H. Weintraub
Publsiher: Elsevier
Total Pages: 408
Release: 2014-02-19
ISBN 10: 0123946174
ISBN 13: 9780123946171
Language: EN, FR, DE, ES & NL

Differential Forms Book Review:

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

Geometry of Differential Forms

Geometry of Differential Forms
Author: Shigeyuki Morita
Publsiher: American Mathematical Soc.
Total Pages: 321
Release: 2001
ISBN 10: 9780821810453
ISBN 13: 0821810456
Language: EN, FR, DE, ES & NL

Geometry of Differential Forms Book Review:

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

Differential Forms
Author: Daniel Abramson
Publsiher: Unknown
Total Pages: 388
Release: 1985
ISBN 10:
ISBN 13: CORNELL:31924000359624
Language: EN, FR, DE, ES & NL

Differential Forms Book Review:

Problems and Solutions in Differential Geometry Lie Series Differential Forms Relativity and Applications

Problems and Solutions in Differential Geometry  Lie Series  Differential Forms  Relativity and Applications
Author: Willi-Hans Steeb
Publsiher: World Scientific Publishing Company
Total Pages: 296
Release: 2017-10-20
ISBN 10: 9813230843
ISBN 13: 9789813230842
Language: EN, FR, DE, ES & NL

Problems and Solutions in Differential Geometry Lie Series Differential Forms Relativity and Applications Book Review:

This volume presents a collection of problems and solutions in differential geometry with applications. Both introductory and advanced topics are introduced in an easy-to-digest manner, with the materials of the volume being self-contained. In particular, curves, surfaces, Riemannian and pseudo-Riemannian manifolds, Hodge duality operator, vector fields and Lie series, differential forms, matrix-valued differential forms, Maurer–Cartan form, and the Lie derivative are covered. Readers will find useful applications to special and general relativity, Yang–Mills theory, hydrodynamics and field theory. Besides the solved problems, each chapter contains stimulating supplementary problems and software implementations are also included. The volume will not only benefit students in mathematics, applied mathematics and theoretical physics, but also researchers in the field of differential geometry. Request Inspection Copy

The Pullback Equation for Differential Forms

The Pullback Equation for Differential Forms
Author: Gyula Csató,Bernard Dacorogna,Olivier Kneuss
Publsiher: Birkhäuser
Total Pages: 436
Release: 2011-11-12
ISBN 10: 9780817683122
ISBN 13: 0817683127
Language: EN, FR, DE, ES & NL

The Pullback Equation for Differential Forms Book Review:

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.

Advanced Calculus

Advanced Calculus
Author: Harold M. Edwards
Publsiher: Springer Science & Business Media
Total Pages: 508
Release: 2013-12-01
ISBN 10: 146120271X
ISBN 13: 9781461202714
Language: EN, FR, DE, ES & NL

Advanced Calculus Book Review:

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.