Celso Melchiades Doria
Differentiability in Banach Spaces, Differential Forms and Applications
Differentiability in Banach Spaces, Differential Forms and Applications
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- More about Differentiability in Banach Spaces, Differential Forms and Applications
The book discusses the theory of differentiable functions between Banach spaces, the differential form formalism, and the Stokes Theorem, with applications to vector fields, flows, harmonic functions, and Maxwell's equations.
Format: Paperback / softback
Length: 362 pages
Publication date: 21 July 2022
Publisher: Springer Nature Switzerland AG
This comprehensive book delves into two distinct parts, each offering a unique perspective on the study of differentiable functions between Banach spaces. The first part focuses on exploring the theory of these functions, while the second part delves into the differential form formalism and its applications.
In the first part, an introductory chapter provides a comprehensive overview of the content, encompassing an introduction to Linear Bounded Operators in Banach Spaces. This chapter serves as a foundation, defining the derivative of Fréchet and presenting examples in Variational Calculus, while also extending the results to Fredholm maps. The Inverse Function Theorem is explained in intricate detail, aiding the reader in comprehending the proof's intricacies and motivations. This first part concludes with a discussion of the inverse function theorem and its diverse applications.
The second part of the book delves into the realm of Vector Fields and Flows. This section begins with an elementary approach to Vector Fields, encompassing the Frobenius Theorem. The Differential Forms are then introduced and applied to obtain the Stokes Theorem and to define De Rham cohomology groups. As an application, the final chapter presents an introduction to Harmonic Functions and adopts a geometric approach to Maxwell's equations of electromagnetism.
Overall, this book serves as a valuable resource for advanced students and researchers in the field of Mathematics, providing a comprehensive and in-depth exploration of differentiable functions between Banach spaces and their applications.
Weight: 575g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030778361
Edition number: 1st ed. 2021
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