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Differentiability in Banach Spaces, Differential Forms and Applications

Authors: Doria, Celso Melchiades

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  • 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 to the formulation of the Maxwell’s equations using differential forms
  • Avoiding complicated notation
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eBook $59.99
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  • ISBN 978-3-030-77834-7
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Hardcover $79.99
price for USA in USD
  • ISBN 978-3-030-77833-0
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  • Usually ready to be dispatched within 3 to 5 business days, if in stock
About this Textbook

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.



About the authors

The author is Professor of Mathematics at the Universidade Federal de Santa Catarina where he is a faculty member since 1993. He holds a PhD title in Mathematics from the University of Warwick, England, under the supervision of Professor James Eells. His research interest lies on Global Analysis, concentrating on the geometry of Gauge Fields and its applications to the Topology and to the Geometry of differentiable manifolds. His scientific background includes a postdoctoral at the Mathematical Institute, Oxford University, England, and another at Michigan State University, USA.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $59.99
price for USA in USD
  • ISBN 978-3-030-77834-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA in USD
  • ISBN 978-3-030-77833-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Differentiability in Banach Spaces, Differential Forms and Applications
Authors
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-77834-7
DOI
10.1007/978-3-030-77834-7
Hardcover ISBN
978-3-030-77833-0
Edition Number
1
Number of Pages
XIV, 362
Number of Illustrations
43 b/w illustrations, 26 illustrations in colour
Topics