Differentiability in Banach Spaces, Differential Forms and Applications (1st ed. 2021)

By: Celso Melchiades Doria

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Synopsis: 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.

Book Quality:: Publisher Quality
ISBN-13:: 9783030778347
Related ISBNs:: 9783030778330
Publisher:: Springer International Publishing
Date of Addition:: 07/21/21
Copyrighted By:: Springer Nature Switzerland AG
Adult content:: No
Language:: English
Has Image Descriptions:: No
Categories:: Nonfiction, Technology, Earth Sciences, Mathematics and Statistics
Submitted By:: Bookshare Staff
Usage Restrictions:: This is a copyrighted book.