國立虎尾科技大學 |

Differentiability in Banach Spaces, Differential Forms and Applications

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Differentiability in Banach Spaces, Differential Forms and Applications / by Celso Melchiades Doria.
Author:	Doria, Celso Melchiades.
Description:	XIV, 362 p. 69 illus., 26 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Global analysis (Mathematics). -
Online resource:	https://doi.org/10.1007/978-3-030-77834-7
ISBN:	9783030778347

Differentiability in Banach Spaces, Differential Forms and Applications
Doria, Celso Melchiades.

Differentiability in Banach Spaces, Differential Forms and Applications [electronic resource] /by Celso Melchiades Doria. - 1st ed. 2021. - XIV, 362 p. 69 illus., 26 illus. in color.online resource.

Introduction -- Chapter 1. Differentiation in R^n -- Chapter 2. Linear Operators in Banach Spaces -- Chapter 3. Differentiation in Banach Spaces -- Chapter 4. Vector Fields -- Chapter 5. Vectors Integration, Potential Theory -- Chapter 6. Differential Forms, Stoke’s Theorem -- Chapter 7. Applications to the Stoke’s Theorem -- Appendix A. Basics of Analysis -- Appendix B. Differentiable Manifolds, Lie Groups -- Appendix C. Tensor Algebra -- Bibliography -- Index.

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.

ISBN: 9783030778347

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

1255807
Global analysis (Mathematics).

LC Class. No.: QA614-614.97

Dewey Class. No.: 514.74

Differentiability in Banach Spaces, Differential Forms and Applications
LDR:02984nam a22003975i 4500 001 1047683
003 DE-He213
005 20210719150623.0
007 cr nn 008mamaa
008 220103s2021 gw | s |||| 0|eng d
020 $a 9783030778347 $9 978-3-030-77834-7
024 7 $a 10.1007/978-3-030-77834-7 $2 doi
035 $a 978-3-030-77834-7
050 4 $a QA614-614.97
072 7 $a PBKS $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKS $2 thema
082 0 4 $a 514.74 $2 23
100 1 $a Doria, Celso Melchiades. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1351417
245 1 0 $a Differentiability in Banach Spaces, Differential Forms and Applications $h [electronic resource] / $c by Celso Melchiades Doria.
250 $a 1st ed. 2021.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a XIV, 362 p. 69 illus., 26 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
505 0 $a Introduction -- Chapter 1. Differentiation in R^n -- Chapter 2. Linear Operators in Banach Spaces -- Chapter 3. Differentiation in Banach Spaces -- Chapter 4. Vector Fields -- Chapter 5. Vectors Integration, Potential Theory -- Chapter 6. Differential Forms, Stoke’s Theorem -- Chapter 7. Applications to the Stoke’s Theorem -- Appendix A. Basics of Analysis -- Appendix B. Differentiable Manifolds, Lie Groups -- Appendix C. Tensor Algebra -- Bibliography -- Index.
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 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.
650 0 $a Global analysis (Mathematics). $3 1255807
650 0 $a Manifolds (Mathematics). $3 1051266
650 0 $a Functional analysis. $3 527706
650 0 $a Calculus. $3 672391
650 0 $a Operator theory. $3 527910
650 0 $a Physics. $3 564049
650 0 $a Engineering mathematics. $3 562757
650 1 4 $a Global Analysis and Analysis on Manifolds. $3 672519
650 2 4 $a Functional Analysis. $3 672166
650 2 4 $a Operator Theory. $3 672127
650 2 4 $a Mathematical Methods in Physics. $3 670749
650 2 4 $a Engineering Mathematics. $3 1203947
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030778330
776 0 8 $i Printed edition: $z 9783030778354
776 0 8 $i Printed edition: $z 9783030778361
856 4 0 $u https://doi.org/10.1007/978-3-030-77834-7
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)