Introduction to Uncertainty Quantification

✍ Scribed by T.J. Sullivan

Publisher: Springer International Publishing
Year: 2015
Tongue: English
Leaves: 351
Series: Texts in Applied Mathematics : 63
Edition: 1st ed.
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xii
Introduction....Pages 1-8
Measure and Probability Theory....Pages 9-34
Banach and Hilbert Spaces....Pages 35-54
Optimization Theory....Pages 55-74
Measures of Information and Uncertainty....Pages 75-90
Bayesian Inverse Problems....Pages 91-112
Filtering and Data Assimilation....Pages 113-131
Orthogonal Polynomials and Applications....Pages 133-164
Numerical Integration....Pages 165-195
Sensitivity Analysis and Model Reduction....Pages 197-222
Spectral Expansions....Pages 223-249
Stochastic Galerkin Methods....Pages 251-276
Non-Intrusive Methods....Pages 277-294
Distributional Uncertainty....Pages 295-318
Back Matter....Pages 319-342

✦ Subjects

Mathematics;Numerical analysis;Mathematical optimization;Probabilities;Physics;Applied mathematics;Engineering mathematics

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