Introduction to Uncertainty Quantification

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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.

Zusammenfassung

One of the first textbooks on the mathematics and statistics of uncertainty quantification

Complete with examples and exercises throughout

Comprehensive with rigorous mathematical details and proofs, but also intuition and motivation

Inhaltsverzeichnis

Introduction.- Measure and Probability Theory.- Banach and Hilbert Spaces.- Optimization Theory.- Measures of Information and Uncertainty.- Bayesian Inverse Problems.- Filtering and Data Assimilation.- Orthogonal Polynomials and Applications.- Numerical Integration.- Sensitivity Analysis and Model Reduction.- Spectral Expansions.- Stochastic Galerkin Methods.- Non-Intrusive Methods.- Distributional Uncertainty.- References.- Index.

Erscheinungsjahr:	2019
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	356
Reihe:	Texts in Applied Mathematics
Inhalt:	xii 342 S. 28 s/w Illustr. 342 p. 28 illus.
ISBN-13:	9783319794785
ISBN-10:	3319794787
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Sullivan, T. J.
Auflage:	Softcover reprint of the original 1st ed. 2015
Hersteller:	Springer International Publishing Texts in Applied Mathematics
Maße:	235 x 155 x 20 mm
Von/Mit:	T. J. Sullivan
Erscheinungsdatum:	13.03.2019
Gewicht:	0,54 kg

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