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Calculus On Normed Vector Spaces

Author: Rodney Coleman
Publisher: Springer Science & Business Media
ISBN: 1461438942
Size: 53.58 MB
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This book serves as an introduction to calculus on normed vector spaces at a higher undergraduate or beginning graduate level. The prerequisites include basic calculus and linear algebra, as well as a certain mathematical maturity. All the important topology and functional analysis topics are introduced where necessary. In its attempt to show how calculus on normed vector spaces extends the basic calculus of functions of several variables, this book is one of the few textbooks to bridge the gap between the available elementary texts and high level texts. The inclusion of many non-trivial applications of the theory and interesting exercises provides motivation for the reader.

Non Associative Normed Algebras

Author: Miguel Cabrera García
Publisher: Cambridge University Press
ISBN: 1107043115
Size: 69.44 MB
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The first systematic account of the basic theory of normed algebras, without assuming associativity. Sure to become a central resource.

Non Associative Normed Algebras Volume 2 Representation Theory And The Zel Manov Approach

Author: Miguel Cabrera García
Publisher: Cambridge University Press
ISBN: 1108570763
Size: 26.42 MB
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This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This second volume revisits JB*-triples, covers Zel'manov's celebrated work in Jordan theory, proves the unit-free variant of the Vidav–Palmer theorem, and develops the representation theory of alternative C*-algebras and non-commutative JB*-algebras. This completes the work begun in the first volume, which introduced these algebras and discussed the so-called non-associative Gelfand–Naimark and Vidav–Palmer theorems. This book interweaves pure algebra, geometry of normed spaces, and infinite-dimensional complex analysis. Novel proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, and an extensive bibliography.

Mathematical Analysis Ii

Author: V. A. Zorich
Publisher: Springer
ISBN: 3662489937
Size: 41.21 MB
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This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis. The main difference between the second and first English editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics. This second volume presents classical analysis in its current form as part of a unified mathematics. It shows how analysis interacts with other modern fields of mathematics such as algebra, differential geometry, differential equations, complex analysis, and functional analysis. This book provides a firm foundation for advanced work in any of these directions.

Analysis Ii

Author: Vladimir A. Zorich
Publisher: Springer
ISBN: 9783540462316
Size: 45.87 MB
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Ausführlich, klar, exakt, solide: die Anfänge der Analysis in 2 Bänden. Von der Einführung der reellen Zahlen bis hin zu fortgeschrittenen Themen wie u.a. Differenzialformen auf Mannigfaltigkeiten, asymptotische Betrachtungen, Fourier-, Laplace- und Legendre-Transformationen, elliptische Funktionen und Distributionen. Deutlich auf naturwissenschaftliche Fragen ausgerichtet, erläutert dieses Werk detailliert Begriffe, Inhalte und Sätze der Integral- und Differenzialrechnung. Die Fülle hilfreicher Beispiele, Aufgaben und Anwendungen ist selten in Analysisbüchern zu finden. Band 2 beschreibt den heutigen Stand der klassischen Analysis.

The Calculus Of Variations

Author: Bruce van Brunt
Publisher: Springer Science & Business Media
ISBN: 0387216979
Size: 22.80 MB
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Suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering, this introduction to the calculus of variations focuses on variational problems involving one independent variable. It also discusses more advanced topics such as the inverse problem, eigenvalue problems, and Noether’s theorem. The text includes numerous examples along with problems to help students consolidate the material.

Analysis Ii

Author: Christiane Tretter
Publisher: Springer-Verlag
ISBN: 3034804768
Size: 16.85 MB
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Das Lehrbuch ist der zweite von zwei einführenden Bänden in die Analysis. Es zeichnet sich dadurch aus, dass alle Themen der Analysis 2 kompakt zusammengefasst sind und dennoch auf typische Schwierigkeiten eingegangen wird. Beginnend mit der Topologie metrischer Räume über die Differentialrechnung von Funktionen mehrerer reeller Variablen bis zu gewöhnlichen Differentialgleichungen und Fourierreihen, enthält das Buch alle prüfungsrelevanten Inhalte. Der Stoff kann anhand von Beispielen, Gegenbeispielen und Aufgaben nachvollzogen werden.

Einf Hrung In Die Komplexe Analysis

Author: Wolfgang Fischer
Publisher: Springer-Verlag
ISBN: 3834893773
Size: 49.18 MB
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In den Bachelor-Studiengängen der Mathematik steht für die Komplexe Analysis (Funktionentheorie) oft nur eine einsemestrige 2-stündige Vorlesung zur Verfügung. Dieses Buch eignet sich als Grundlage für eine solche Vorlesung im 2. Studienjahr. Mit einer guten thematischen Auswahl, vielen Beispielen und ausführlichen Erläuterungen gibt dieses Buch eine Darstellung der Komplexen Analysis, die genau die Grundlagen und den wesentlichen Kernbestand dieses Gebietes enthält. Das Buch bietet über diese Grundausbildung hinaus weiteres Lehrmaterial als Ergänzung, sodass es auch für eine 3- oder 4 –stündige Vorlesung geeignet ist. Je nach Hörerkreis kann der Stoff unterschiedlich erweitert werden. So wurden für den „Bachelor Lehramt“ die geometrischen Aspekte der Komplexen Analysis besonders herausgearbeitet.