Differential Forms and Applications
Differential Forms and Applications

Author: Manfredo P. Do Carmo

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 124

ISBN-13: 3642579515

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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 and Applications
Differential Forms and Applications

Author: Manfredo P. Do Carmo

Publisher: Springer Science & Business Media

Published: 1998-05-20

Total Pages: 136

ISBN-13: 9783540576181

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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 and Connections
Differential Forms and Connections

Author: R. W. R. Darling

Publisher: Cambridge University Press

Published: 1994-09-22

Total Pages: 288

ISBN-13: 9780521468008

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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.

Differentiability in Banach Spaces, Differential Forms and Applications
Differentiability in Banach Spaces, Differential Forms and Applications

Author: Celso Melchiades Doria

Publisher: Springer Nature

Published: 2021-07-19

Total Pages: 362

ISBN-13: 3030778347

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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.

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: Springer

Published: 2018-11-03

Total Pages: 470

ISBN-13: 3319969927

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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.

A Geometric Approach to Differential Forms
A Geometric Approach to Differential Forms

Author: David Bachman

Publisher: Springer Science & Business Media

Published: 2012-02-02

Total Pages: 167

ISBN-13: 0817683046

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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: Academic Press

Published: 1997

Total Pages: 50

ISBN-13: 9780127425108

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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

Exterior Analysis
Exterior Analysis

Author: Erdogan Suhubi

Publisher: Elsevier

Published: 2013-09-13

Total Pages: 780

ISBN-13: 0124159281

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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

Tensors, Differential Forms, and Variational Principles
Tensors, Differential Forms, and Variational Principles

Author: David Lovelock

Publisher: Courier Corporation

Published: 2012-04-20

Total Pages: 402

ISBN-13: 048613198X

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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 Geometry with Applications to Mechanics and Physics
Differential Geometry with Applications to Mechanics and Physics

Author: Yves Talpaert

Publisher: CRC Press

Published: 2000-09-12

Total Pages: 480

ISBN-13: 9780824703851

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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.