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9781611972474 Academic Inspection Copy

Computational Mathematical Modeling

An Integrated Approach Across Scales
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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 probablistic methodologies that are naturally bridged through examples. Painlessly introduces students to advanced themes in a natural progression. Includes suggestions for further reading.
Daniela Calvetti is a 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 100 research papers and one monograph. Erkki Somersalo is a Professor 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. He has published two monographs and over a hundred research papers.
Chapter 1: Review of Multivariate Calculus and Differential Equations Chapter 2: Compartment Models Chapter 3: From Compartment Models to Continuous Models Chapter 4: Dimensional Analysis and Scaling Chapter 5: Introduction to Stochastic Modeling Chapter 6: Modeling of Noise Chapter 7: Modeling with Waiting Processes Chapter 8: Markov Processes Chapter 9: Cellular Automata, Agent Based Modeling
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