Linear Functional Analysis

Author: Bryan Rynne,M.A. Youngson

Publisher: Springer Science & Business Media

ISBN: 1447136551

Category: Mathematics

Page: 273

View: 1561

This book provides an introduction to the ideas and methods of linear func tional analysis at a level appropriate to the final year of an undergraduate course at a British university. The prerequisites for reading it are a standard undergraduate knowledge of linear algebra and real analysis (including the the ory of metric spaces). Part of the development of functional analysis can be traced to attempts to find a suitable framework in which to discuss differential and integral equa tions. Often, the appropriate setting turned out to be a vector space of real or complex-valued functions defined on some set. In general, such a vector space is infinite-dimensional. This leads to difficulties in that, although many of the elementary properties of finite-dimensional vector spaces hold in infinite dimensional vector spaces, many others do not. For example, in general infinite dimensional vector spaces there is no framework in which to make sense of an alytic concepts such as convergence and continuity. Nevertheless, on the spaces of most interest to us there is often a norm (which extends the idea of the length of a vector to a somewhat more abstract setting). Since a norm on a vector space gives rise to a metric on the space, it is now possible to do analysis in the space. As real or complex-valued functions are often called functionals, the term functional analysis came to be used for this topic. We now briefly outline the contents of the book.
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Introduction to Uncertainty Quantification

Author: T.J. Sullivan

Publisher: Springer

ISBN: 3319233955

Category: Mathematics

Page: 342

View: 8141

This text provides a framework in which the main objectives of the field of uncertainty quantification (UQ) are defined and an overview of the range of mathematical methods by which they can be achieved. Complete with exercises throughout, the book will equip readers with both theoretical understanding and practical experience of the key mathematical and algorithmic tools underlying the treatment of uncertainty in modern applied mathematics. Students and readers alike are encouraged to apply the mathematical methods discussed in this book to their own favorite problems to understand their strengths and weaknesses, also making the text suitable for a self-study. Uncertainty quantification is a topic of increasing practical importance at the intersection of applied mathematics, statistics, computation and numerous application areas in science and engineering. This text is designed as an introduction to UQ for senior undergraduate and graduate students with a mathematical or statistical background and also for researchers from the mathematical sciences or from applications areas who are interested in the field. T. J. Sullivan was Warwick Zeeman Lecturer at the Mathematics Institute of the University of Warwick, United Kingdom, from 2012 to 2015. Since 2015, he is Junior Professor of Applied Mathematics at the Free University of Berlin, Germany, with specialism in Uncertainty and Risk Quantification.
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Kernel-based Approximation Methods using MATLAB

Author: Gregory Fasshauer,Michael McCourt

Publisher: World Scientific Publishing Company

ISBN: 9814630152

Category: Mathematics

Page: 536

View: 5663

In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in various settings. The authors explore the historical context of this fascinating topic and explain recent advances as strategies to address long-standing problems. Examples are drawn from fields as diverse as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling and finance. Researchers from those and other fields can recreate the results within using the documented MATLAB code, also available through the online library. This combination of a strong theoretical foundation and accessible experimentation empowers readers to use positive definite kernels on their own problems of interest.
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Lineare Funktionalanalysis

Eine anwendungsorientierte Einführung

Author: Hans Wilhelm Alt

Publisher: Springer-Verlag

ISBN: 3662083868

Category: Mathematics

Page: 294

View: 8459

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Partielle Differentialgleichungen der Geometrie und der Physik 2

Funktionalanalytische Lösungsmethoden

Author: Friedrich Sauvigny

Publisher: Springer-Verlag

ISBN: 3540275401

Category: Mathematics

Page: 350

View: 6376

Das zweibändige Lehrbuch behandelt das Gebiet der partiellen Differentialgleichungen umfassend und anschaulich. Der Autor stellt in Band 2 funktionalanalytische Lösungsmethoden vor und erläutert u. a. die Lösbarkeit von Operatorgleichungen im Banachraum, lineare Operatoren im Hilbertraum und Spektraltheorie, die Schaudersche Theorie linearer elliptischer Differentialgleichungen sowie schwache Lösungen elliptischer Differentialgleichungen.
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Applied Functional Analysis

Applications to Mathematical Physics

Author: Eberhard Zeidler

Publisher: Springer Science & Business Media

ISBN: 1461208157

Category: Mathematics

Page: 481

View: 4969

The first part of a self-contained, elementary textbook, combining linear functional analysis, nonlinear functional analysis, numerical functional analysis, and their substantial applications with each other. As such, the book addresses undergraduate students and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world. Applications concern ordinary and partial differential equations, the method of finite elements, integral equations, special functions, both the Schroedinger approach and the Feynman approach to quantum physics, and quantum statistics. As a prerequisite, readers should be familiar with some basic facts of calculus. The second part has been published under the title, Applied Functional Analysis: Main Principles and Their Applications.
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Special Relativity

Author: Nicholas M.J. Woodhouse

Publisher: Springer-Verlag

ISBN: 3540466762

Category: Science

Page: 88

View: 6896

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Real and Functional Analysis

Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 1461208971

Category: Mathematics

Page: 580

View: 4720

This book is meant as a text for a first-year graduate course in analysis. In a sense, it covers the same topics as elementary calculus but treats them in a manner suitable for people who will be using it in further mathematical investigations. The organization avoids long chains of logical interdependence, so that chapters are mostly independent. This allows a course to omit material from some chapters without compromising the exposition of material from later chapters.
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Distributionen Und Hilbertraumoperatoren

Mathematische Methoden Der Physik

Author: Philippe Blanchard,Erwin Brüning

Publisher: Springer

ISBN: 9783211825075

Category: Science

Page: 375

View: 3779

Das Buch bietet eine Einführung in die zum Studium der Theoretischen Physik notwendigen mathematischen Grundlagen. Der erste Teil des Buches beschäftigt sich mit der Theorie der Distributionen und vermittelt daneben einige Grundbegriffe der linearen Funktionalanalysis. Der zweite Teil baut darauf auf und gibt eine auf das Wesentliche beschränkte Einführung in die Theorie der linearen Operatoren in Hilbert-Räumen. Beide Teile werden von je einer Übersicht begleitet, die die zentralen Ideen und Begriffe knapp erläutert und den Inhalt kurz beschreibt. In den Anhängen werden einige grundlegende Konstruktionen und Konzepte der Funktionalanalysis dargestellt und wichtige Konsequenzen entwickelt.
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Einführung in die Funktionalanalysis

Author: Reinhold Meise,Dietmar Vogt

Publisher: Springer-Verlag

ISBN: 3322803104

Category: Mathematics

Page: 416

View: 4629

Dieses Buch wendet sich an Studenten der Mathematik und der Physik, welche über Grundkenntnisse in Analysis und linearer Algebra verfügen.
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Moderne Algebra

Author: Bartel Eckmann L. Van der van der Waerden,Emil Artin,Emmy Noether

Publisher: Springer-Verlag

ISBN: 3662364344

Category: Mathematics

Page: 274

View: 5828

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
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Introductory Functional Analysis

With Applications to Boundary Value Problems and Finite Elements

Author: B.D. Reddy

Publisher: Springer Science & Business Media

ISBN: 1461205751

Category: Mathematics

Page: 472

View: 1373

Providing an introduction to functional analysis, this text treats in detail its application to boundary-value problems and finite elements, and is distinguished by the fact that abstract concepts are motivated and illustrated wherever possible. It is intended for use by senior undergraduates and graduates in mathematics, the physical sciences and engineering, who may not have been exposed to the conventional prerequisites for a course in functional analysis, such as real analysis. Mature researchers wishing to learn the basic ideas of functional analysis will equally find this useful. Offers a good grounding in those aspects of functional analysis which are most relevant to a proper understanding and appreciation of the mathematical aspects of boundary-value problems and the finite element method.
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Functional Analysis, Spectral Theory, and Applications

Author: Manfred Einsiedler,Thomas Ward

Publisher: Springer

ISBN: 3319585401

Category: Mathematics

Page: 614

View: 3220

This textbook provides a careful treatment of functional analysis and some of its applications in analysis, number theory, and ergodic theory. In addition to discussing core material in functional analysis, the authors cover more recent and advanced topics, including Weyl’s law for eigenfunctions of the Laplace operator, amenability and property (T), the measurable functional calculus, spectral theory for unbounded operators, and an account of Tao’s approach to the prime number theorem using Banach algebras. The book further contains numerous examples and exercises, making it suitable for both lecture courses and self-study. Functional Analysis, Spectral Theory, and Applications is aimed at postgraduate and advanced undergraduate students with some background in analysis and algebra, but will also appeal to everyone with an interest in seeing how functional analysis can be applied to other parts of mathematics.
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Real Analysis for the Undergraduate

With an Invitation to Functional Analysis

Author: Matthew A. Pons

Publisher: Springer Science & Business Media

ISBN: 1461496381

Category: Mathematics

Page: 409

View: 2619

This undergraduate textbook introduces students to the basics of real analysis, provides an introduction to more advanced topics including measure theory and Lebesgue integration, and offers an invitation to functional analysis. While these advanced topics are not typically encountered until graduate study, the text is designed for the beginner. The author’s engaging style makes advanced topics approachable without sacrificing rigor. The text also consistently encourages the reader to pick up a pencil and take an active part in the learning process. Key features include: - examples to reinforce theory; - thorough explanations preceding definitions, theorems and formal proofs; - illustrations to support intuition; - over 450 exercises designed to develop connections between the concrete and abstract. This text takes students on a journey through the basics of real analysis and provides those who wish to delve deeper the opportunity to experience mathematical ideas that are beyond the standard undergraduate curriculum.
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Approximation

Author: Armin Iske

Publisher: Springer-Verlag

ISBN: 3662554658

Category: Mathematics

Page: 360

View: 6193

Dieses Lehrbuch bietet eine anschauliche Einführung in die Theorie und Numerik der Approximation mit Bezügen zu aktuellen Anwendungen der Datenanalyse. Dabei werden klassische Themen der Approximation mit relevanten Methoden der mathematischen Signalverarbeitung verknüpft und gut nachvollziehbar erklärt. Bei den Herleitungen der verschiedenen Approximationsmethoden werden konstruktive Zugänge bevorzugt. Dies führt direkt zu numerischen Algorithmen, deren Implementierung im Detail erklärt wird. Weiterhin illustriert eine Vielzahl an Beispielen die theoretischen und numerischen Grundlagen. Das Lehrbuch behandelt u.a. folgende Themen: Bestapproximationen in normierten linearen Räumen Approximation in euklidischen Räumen Tschebyscheff-Approximation Asymptotische Resultate der Approximation Kern-basierte Approximation mit gitterfreien Methoden Approximationsmethoden der Computertomographie Neben zahlreichen Beispielen sind für die weitere Vertiefung der Kernthemen auch viele Übungsaufgaben mit Lösungshinweisen enthalten.
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Theoretical Numerical Analysis

A Functional Analysis Framework

Author: Kendall Atkinson,Weimin Han

Publisher: Springer Science & Business Media

ISBN: 9780387258874

Category: Mathematics

Page: 576

View: 8557

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). Thedevelopmentofnewcoursesisanaturalconsequenceofahighlevelof excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Ma- ematical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs.
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