"You cannot understand the physical world in any deep or
satisfying way without using mathematical reasoning..." -- R. P. Feynman
"No human investigation can be called real science if it cannot be
demonstrated mathematically." -- Leonardo da
Vinci (translated from Italian)
This course will present an introduction and survey of mathematical models
for problems in the applied sciences and engineering. The real-world problems,
coming from areas like mechanical systems, control theory, bio-chemical
reactions, and heat transfer will be formulated as idealized mathematical
models. Equations will be derived from first principles in geometry, physics
and the calculus of variations. Mathematical techniques such as
nondimensionalization, perturbation analysis, and self-similar solutions
will then be introduced to simplify the models and yield insight into
the underlying problems.
