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Titlebook: Differentiability in Banach Spaces, Differential Forms and Applications; Celso Melchiades Doria Textbook 2021 Springer Nature Switzerland

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書目名稱Differentiability in Banach Spaces, Differential Forms and Applications
編輯Celso Melchiades Doria
視頻videohttp://file.papertrans.cn/279/278626/278626.mp4
概述The differential forms formalism is explained through the classical theorems of integrations and applied to obtain topological invariants.Includes applications to the study of harmonic functions and t
圖書封面Titlebook: Differentiability in Banach Spaces, Differential Forms and Applications;  Celso Melchiades Doria Textbook 2021 Springer Nature Switzerland
描述.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 finalchapter contains an introduction to the Harmonic Functions and a geometric approach to Maxwell‘s equations of electromagnetism..
出版日期Textbook 2021
關(guān)鍵詞Banach Space; Differential of Functions; Differential Forms; Harmonic Functions; Harmonic Forms; De Rham
版次1
doihttps://doi.org/10.1007/978-3-030-77834-7
isbn_softcover978-3-030-77836-1
isbn_ebook978-3-030-77834-7
copyrightSpringer Nature Switzerland AG 2021
The information of publication is updating

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Vector Integration, Potential Theory,ormalism allows us to generalize the Stokes Theorem to describe the conditions of integrability (Frobenius Theorem), and to write Maxwell’s equations succinctly to obtain topological invariants using differentiable tools and many other applications.
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Differentiability in Banach Spaces, Differential Forms and Applications978-3-030-77834-7
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em. The Differential Forms are introduced and applied to obtain the Stokes Theorem and to define De Rham cohomology groups. As an application, the finalchapter contains an introduction to the Harmonic Functions and a geometric approach to Maxwell‘s equations of electromagnetism..978-3-030-77836-1978-3-030-77834-7
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