Computational Mathematical Modeling: An Integrated Approach Across Scales
An Integrated Approach Across Scales
Monographs on Mathematical Modeling and Computation Series

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.

Preface; 1. Review of multivariate calculus and differential equations; 2. Compartment models; 3. From compartment models to continuous models; 4. Dimensional analysis and scaling; 5. Introduction to stochastic modeling; 6. Modeling of noise; 7. Modeling with waiting processes; 8. Markov processes; 9. Cellular automata, agent-based modeling; Bibliography; Index.

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.