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Beschreibung
These volumes introduce and develop the theory of linear structures for students of mathematics and its applications. Today, linear algebra serves as an essential tool and unifying language across nearly all areas of mathematics. Given its importance in the natural sciences, engineering, and economics, linear algebra is presented as a valuable and widely applicable subject in its own right.… Adopting an inductive approach while maintaining an appropriate level of abstraction, the volumes lead the reader from finite-dimensional vector spaces over the fields ℝ and ℂ to general fields and infinite-dimensional vector spaces . Throughout, the principal examples are the tuple space ℝ n , matrix spaces, and solution spaces of systems of linear equations. To preserve accessibility, the exposition does not follow a strictly deductive development. Instead, inductive elements are incorporated throughout. In the first chapter, margin notes indicate where the theory is developed through the study of systems of linear equations. Further margin notes indicate where the general theory is applied to systems of linear equations. Different methods of proof are used to illuminate the same topic from complementary perspectives. A recurring theme is the algorithmic viewpoint, emphasizing practical methods and numerical complexity without sacrificing structural understanding. The discussion therefore begins with the theoretical insights provided by Gaussian elimination and develops the corresponding structural concepts alongside computational techniques. In addition to the standard core material, the volume includes topics of interest to students from a variety of disciplines. Students of mathematics education will find an introduction to several aspects of analytic geometry, beginning in this first volume with affine geometry. Readers drawn to algebra are introduced not only to the theory of vector spaces over a field K , but also to more general algebraic structures. For students pursuing numerical mathematics, optimization, or applications outside mathematics, topics such as LU decomposition, least-squares problems and the pseudoinverse are discussed. For students of physics a series of examples incorporates the linear algebra related aspects of a first year physics course. Particular emphasis is placed on connecting theory and algorithms and on relating both to applications in the sciences. To support this goal, mathematical modelling plays a central role. Ongoing examples drawn from mechanics, electrical networks, and economics are developed progressively alongside the theory. An additional running example explores historical questions. Dieses Produkt haben wir gerade leider nicht auf Lager.
Handgeprüfte Gebrauchtware
Bis zu 50 % günstiger als neu
21 Tage Widerrufsrecht
Technische Daten
Erscheinungsdatum
27.02.2027
Sprache
Englisch
EAN
9783032414724
Herausgeber
Springer International Publishing
Sonderedition
Nein
Autor
Peter Knabner, Wolf Barth
Seitenanzahl
540
Einbandart
Gebundene Ausgabe
Buch Untertitel
Foundations and Applications: The Basics
Schlagwörter
linear algebra, matrix theory, linear systems of equations, numerical linear algebra, linear structures
Thema-Inhalt
PB - Mathematik
Höhe
235 mm
Breite
15.5 cm
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Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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