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Full Description
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.
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
