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Differentiability in spaces, differe...

Doria, Celso Melchiades.

Differentiability in spaces, differential forms and applications

Record Type:	Electronic resources : Monograph/item
Title/Author:	Differentiability in spaces, differential forms and applicationsby Celso Melchiades Doria.
Author:	Doria, Celso Melchiades.
Published:	Cham :Springer International Publishing :2021.
Description:	xiv, 362 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Banach spaces.
Online resource:	https://doi.org/10.1007/978-3-030-77834-7
ISBN:	9783030778347$q(electronic bk.)

Differentiability in spaces, differential forms and applications
Doria, Celso Melchiades.

Differentiability in spaces, differential forms and applications[electronic resource] /by Celso Melchiades Doria. - Cham :Springer International Publishing :2021. - xiv, 362 p. :ill., digital ;24 cm.

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 Frechet 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.

ISBN: 9783030778347$q(electronic bk.)

Standard No.: 10.1007/978-3-030-77834-7doiSubjects--Topical Terms:

199048
Banach spaces.

LC Class. No.: QA322.2

Dewey Class. No.: 515.732

Differentiability in spaces, differential forms and applications
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245 1 0 $a Differentiability in spaces, differential forms and applications $h [electronic resource] / $c by Celso Melchiades Doria.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a xiv, 362 p. : $b ill., digital ; $c 24 cm.
520 $a 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 Frechet 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.
650 0 $a Banach spaces. $3 199048
650 0 $a Stokes' theorem. $3 901712
650 1 4 $a Global Analysis and Analysis on Manifolds. $3 273786
650 2 4 $a Functional Analysis. $3 274845
650 2 4 $a Calculus. $3 183091
650 2 4 $a Operator Theory. $3 274795
650 2 4 $a Mathematical Methods in Physics. $3 273796
650 2 4 $a Engineering Mathematics. $3 806481
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950 $a Mathematics and Statistics (SpringerNature-11649)