Broadly speaking, there are two general approaches to teaching
mathematical modeling: 1) the case study approach, and 2) the
method based approach (that teaches mathematical techniques with
applications to relevant mathematical models). This text emphasizes
instead the scientific issues for modeling different phenomena. For
the natural or harvested growth of a fish population, we may be
interested in the evolution of the population, whether it reaches a
steady state (equilibrium or cycle), stable or unstable with
respect to a small perturbation from equilibrium, or whether a
small change in the environment would cause a catastrophic change,
etc. Each scientific issue requires an appropriate model and a
different set of mathematical tools to extract information from the
model. Models examined are chosen to help explain or justify
empirical observations such as cocktail drug treatments are more
effective and regenerations after injuries or illness are
fast-tracked (compared to original developments).Volume I of this
three-volume set limits its scope to phenomena and scientific
issues that are modeled by ordinary differential equations (ODE).
Scientific issues such as signal and wave propagation, diffusion,
and shock formation involving spatial dynamics to be modeled by
partial differential equations (PDE) will be treated in Vol. II.
Scientific issues involving randomness and uncertainty are examined
in Vol. III.
General
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