Daniela Calvetti
College of Arts & Sciences
Department of Mathematics, Applied Mathematics, & Statistics
http://math.case.edu/faculty/daniela-calvetti/
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Introduction to Bayesian Scientific Computing: ten lectures on subjective computing by Erkki Somersalo; Daniela CalvettiISBN: 9780387733937
Publication Date: 2007-11-26
This book has been written for undergraduate and graduate students in various disciplines of mathematics. The authors, internationally recognized experts in their field, have developed a superior teaching and learning tool that makes it easy to grasp new concepts and apply them in practice. The book's highly accessible approach makes it particularly ideal if you want to become acquainted with the Bayesian approach to computational science, but do not need to be fully immersed in detailed statistical analysis.
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Computational Mathematical Modeling: an integrated approach across scales by Daniela Calvetti; Erkki SomersaloISBN: 9781611972474
Publication Date: 2013-01-01
Interesting real-world mathematical modeling problems are complex and can usually be studied at different scales. The scale at which the investigation is carried out is one of the factors that determines the type of mathematics most appropriate to describe the problem. The book concentrates on two modeling paradigms: the macroscopic, in which phenomena are described in terms of time evolution via ordinary differential equations; and the microscopic, which requires knowledge of random events and probability. The exposition is based on this unorthodox combination of deterministic and probabilistic methodologies, and emphasizes the development of computational skills to construct predictive models. To elucidate the concepts, a wealth of examples, self-study problems, and portions of MATLAB code used by the authors are included. This book, which has been extensively tested by the authors for classroom use, is intended for students in mathematics and the physical sciences at the advanced undergraduate level and above.