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＜電子ブック＞
Introduction to Uncertainty Quantification / by T.J. Sullivan
(Texts in Applied Mathematics. ISSN:21969949 ; 63)

版	1st ed. 2015.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2015
大きさ	XII, 342 p. 28 illus : online resource
著者標目	*Sullivan, T.J author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Mathematical optimization LCSH:Numerical analysis LCSH:Engineering mathematics LCSH:Engineering—Data processing LCSH:Mathematical physics FREE:Probability Theory FREE:Optimization FREE:Numerical Analysis FREE:Mathematical and Computational Engineering Applications FREE:Theoretical, Mathematical and Computational Physics
一般注記	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 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 provides a framework in which the main objectives of the field of uncertainty quantification 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 favourite problems to understand their strengths and weaknesses, also making the text suitable as a self-study. This text is designed as an introduction to uncertainty quantification 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 HTTP:URL=https://doi.org/10.1007/978-3-319-23395-6

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