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Computational Mathematical Modeling: An Integrated Approach Across Scales Click on picture to view full-size image Computational Mathematical Modeling: An Integrated Approach Across Scales

Daniela Calvetti and Erkki Somersalo



Mathematical Modeling and Computation 17

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 the authors describe phenomena in terms of time evolution via ordinary differential equations, and the microscopic, which requires knowledge of random events and probability. The text emphasizes the development of computational skills to construct predictive models and analyze the results. To elucidate the concepts, a wealth of examples and portions of MATLAB® code used by the authors are included.

Computational Mathematical Modeling: An Integrated Approach Across Scales
• is designed for classroom use, has been extensively tested by the authors, and has homework problems carefully designed to develop students’ computational skills;
• is based on an unorthodox combination of deterministic and probabilistic methodologies that are naturally bridged through examples;
• painlessly introduces students to advanced themes in a natural progression; and
• includes suggestions for further reading.

Audience
This book is intended for advanced undergraduate and beginning graduate students in mathematics, engineering, and physical and life sciences.


About the Authors
Daniela Calvetti is Professor of Mathematics at Case Western Reserve University. Her research interests include numerical linear algebra, large scale scientific computing, Bayesian statistical computing, and modeling. She has published over one hundred research papers and a monograph.

Erkki Somersalo is Professor of Mathematics at Case Western Reserve University. His areas of expertise are computational inverse problems, statistical scientific computing, and fields and waves, in particular with applications to medical imaging. His work also includes applications in life sciences and medicine. His publications include two monographs and over one hundred articles.


Contents
Preface
Index


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Keywords
probability, ordinary differential equations, scaling, dimensional analysis, agent based modeling


2013 / x + 224 pages / Softcover / ISBN 978-1-611972-47-4
List Price $69.00 / SIAM Member Price $48.30 / Order Code MM17
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