國立虎尾科技大學 |

Functional Analysis Tools for Practical Use in Sciences and Engineering

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Functional Analysis Tools for Practical Use in Sciences and Engineering/ by Carlos A. de Moura.
Author:	de Moura, Carlos A.
Description:	XVII, 214 p. 16 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Functional analysis. -
Online resource:	https://doi.org/10.1007/978-3-031-10598-2
ISBN:	9783031105982

Functional Analysis Tools for Practical Use in Sciences and Engineering
de Moura, Carlos A.

Functional Analysis Tools for Practical Use in Sciences and Engineering[electronic resource] /by Carlos A. de Moura. - 1st ed. 2022. - XVII, 214 p. 16 illus.online resource.

Road Map -- Basic Concepts -- Dual of a Normed Space -- Sobolev Spaces, Distributions -- The Three Basic Principles -- Compactness -- Function Derivatives in Normed Spaces -- Hilbert Bases and Approximations.

This textbook describes selected topics in functional analysis as powerful tools of immediate use in many fields within applied mathematics, physics and engineering. It follows a very reader-friendly structure, with the presentation and the level of exposition especially tailored to those who need functional analysis but don’t have a strong background in this branch of mathematics. For every tool, this work emphasizes the motivation, the justification for the choices made, and the right way to employ the techniques. Proofs appear only when necessary for the safe use of the results. The book gently starts with a road map to guide reading. A subsequent chapter recalls definitions and notation for abstract spaces and some function spaces, while Chapter 3 enters dual spaces. Tools from Chapters 2 and 3 find use in Chapter 4, which introduces distributions. The Linear Functional Analysis basic triplet makes up Chapter 5, followed by Chapter 6, which introduces the concept of compactness. Chapter 7 brings a generalization of the concept of derivative for functions defined in normed spaces, while Chapter 8 discusses basic results about Hilbert spaces that are paramount to numerical approximations. The last chapter brings remarks to recent bibliographical items. Elementary examples included throughout the chapters foster understanding and self-study. By making key, complex topics more accessible, this book serves as a valuable resource for researchers, students, and practitioners alike that need to rely on solid functional analysis but don’t need to delve deep into the underlying theory.

ISBN: 9783031105982

Standard No.: 10.1007/978-3-031-10598-2doiSubjects--Topical Terms:

527706
Functional analysis.

LC Class. No.: QA319-329.9

Dewey Class. No.: 515.7

Functional Analysis Tools for Practical Use in Sciences and Engineering
LDR:03185nam a22003975i 4500 001 1084251
003 DE-He213
005 20221013160907.0
007 cr nn 008mamaa
008 221228s2022 sz | s |||| 0|eng d
020 $a 9783031105982 $9 978-3-031-10598-2
024 7 $a 10.1007/978-3-031-10598-2 $2 doi
035 $a 978-3-031-10598-2
050 4 $a QA319-329.9
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.7 $2 23
100 1 $a de Moura, Carlos A. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1390497
245 1 0 $a Functional Analysis Tools for Practical Use in Sciences and Engineering $h [electronic resource] / $c by Carlos A. de Moura.
250 $a 1st ed. 2022.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a XVII, 214 p. 16 illus. $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 Road Map -- Basic Concepts -- Dual of a Normed Space -- Sobolev Spaces, Distributions -- The Three Basic Principles -- Compactness -- Function Derivatives in Normed Spaces -- Hilbert Bases and Approximations.
520 $a This textbook describes selected topics in functional analysis as powerful tools of immediate use in many fields within applied mathematics, physics and engineering. It follows a very reader-friendly structure, with the presentation and the level of exposition especially tailored to those who need functional analysis but don’t have a strong background in this branch of mathematics. For every tool, this work emphasizes the motivation, the justification for the choices made, and the right way to employ the techniques. Proofs appear only when necessary for the safe use of the results. The book gently starts with a road map to guide reading. A subsequent chapter recalls definitions and notation for abstract spaces and some function spaces, while Chapter 3 enters dual spaces. Tools from Chapters 2 and 3 find use in Chapter 4, which introduces distributions. The Linear Functional Analysis basic triplet makes up Chapter 5, followed by Chapter 6, which introduces the concept of compactness. Chapter 7 brings a generalization of the concept of derivative for functions defined in normed spaces, while Chapter 8 discusses basic results about Hilbert spaces that are paramount to numerical approximations. The last chapter brings remarks to recent bibliographical items. Elementary examples included throughout the chapters foster understanding and self-study. By making key, complex topics more accessible, this book serves as a valuable resource for researchers, students, and practitioners alike that need to rely on solid functional analysis but don’t need to delve deep into the underlying theory.
650 0 $a Functional analysis. $3 527706
650 0 $a Sequences (Mathematics). $3 1253882
650 0 $a Mathematical analysis. $3 527926
650 1 4 $a Functional Analysis. $3 672166
650 2 4 $a Sequences, Series, Summability. $3 672022
650 2 4 $a Integral Transforms and Operational Calculus. $3 1366597
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783031105975
776 0 8 $i Printed edition: $z 9783031105999
776 0 8 $i Printed edition: $z 9783031106002
856 4 0 $u https://doi.org/10.1007/978-3-031-10598-2
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)