Applications of Functional Analysis in Engineering: 22 (Mathematical Concepts and Methods in Science and Engineering) - Softcover

Nowinski, J.

 
9781468439281: Applications of Functional Analysis in Engineering: 22 (Mathematical Concepts and Methods in Science and Engineering)
Softcover
ISBN 10: 1468439286 ISBN 13: 9781468439281
Verlag: Springer, 2012

Inhaltsangabe

Functional analysis owes its OrIgms to the discovery of certain striking analogies between apparently distinct disciplines of mathematics such as analysis, algebra, and geometry. At the turn of the nineteenth century, a number of observations, made sporadically over the preceding years, began to inspire systematic investigations into the common features of these three disciplines, which have developed rather independently of each other for so long. It was found that many concepts of this triad-analysis, algebra, geometry-could be incorporated into a single, but considerably more abstract, new discipline which came to be called functional analysis. In this way, many aspects of analysis and algebra acquired unexpected and pro­ found geometric meaning, while geometric methods inspired new lines of approach in analysis and algebra. A first significant step toward the unification and generalization of algebra, analysis, and geometry was taken by Hilbert in 1906, who studied the collection, later called 1 , composed of infinite sequences x = Xb X 2, ... , 2 X , ... , of numbers satisfying the condition that the sum Ik"= 1 X 2 converges. k k The collection 12 became a prototype of the class of collections known today as Hilbert spaces.

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Reseña del editor

Functional analysis owes its OrIgms to the discovery of certain striking analogies between apparently distinct disciplines of mathematics such as analysis, algebra, and geometry. At the turn of the nineteenth century, a number of observations, made sporadically over the preceding years, began to inspire systematic investigations into the common features of these three disciplines, which have developed rather independently of each other for so long. It was found that many concepts of this triad-analysis, algebra, geometry-could be incorporated into a single, but considerably more abstract, new discipline which came to be called functional analysis. In this way, many aspects of analysis and algebra acquired unexpected and pro­ found geometric meaning, while geometric methods inspired new lines of approach in analysis and algebra. A first significant step toward the unification and generalization of algebra, analysis, and geometry was taken by Hilbert in 1906, who studied the collection, later called 1 , composed of infinite sequences x = Xb X 2, ... , 2 X , ... , of numbers satisfying the condition that the sum Ik"= 1 X 2 converges. k k The collection 12 became a prototype of the class of collections known today as Hilbert spaces.

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Verlag
Springer
Erscheinungsdatum
2012
Sprache
Englisch
ISBN 10 
1468439286
ISBN 13 
9781468439281
Einband
Tapa blanda
Anzahl der Seiten
324
Kontakt zum Hersteller
Nicht verfügbar
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Weitere beliebte Ausgaben desselben Titels

9780306406935: Application of Functional Analysis in Engineering: 22 (Mathematical Concepts and Methods in Science and Engineering)

Vorgestellte Ausgabe

ISBN 10:  0306406934 ISBN 13:  9780306406935
Verlag: Kluwer Academic / Plenum Publishers, 1981
Hardcover