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Differentiability in spaces, differe...

Doria, Celso Melchiades.

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Differentiability in spaces, differential forms and applications

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Differentiability in spaces, differential forms and applications/ by Celso Melchiades Doria.
作者:	Doria, Celso Melchiades.
出版者:	Cham :Springer International Publishing : : 2021.,
面頁冊數:	xiv, 362 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Banach spaces. -
電子資源:	https://doi.org/10.1007/978-3-030-77834-7
ISBN:	9783030778347

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

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

579190
Banach spaces.

LC Class. No.: QA322.2

Dewey Class. No.: 515.732

Differentiability in spaces, differential forms and applications
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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.
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