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

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. This 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 and has been extensively tested by the authors. The homework problems have been carefully designed to develop students computational skills. The book is based on an unorthodox combination of deterministic and probablistic methodologies that are naturally bridged through examples; it 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.

Contents 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