Q. Why should (a) engineers, (b) physicists, (c)
mathematicians
take Math 5451?
A. Math 5451 occupies a
prominent
and natural role in
the engineering arts, in physics, in mathematics,
etc.
(a) In the engineering arts optimization
processes on infinite dimensional parameter spaces and their
finite
dimensional approximations, open new conceptual vistas
which would remain inaccessible
within the framework of finite-dimensional calculus.
(b) In physics Math
5451 furnishes,
among others, very powerful extremum principles. By cutting across
diverse
aspects of nature, these principles allow, for example, a
grasp
of classical and wave mechanics
from
a
single perspective and with respect to any coordinate frame.
(c) For mathematics Math 5451 provides a
natural connecting link between theoretical
mathematics
(e.g.
global
analysis, differential geometry, etc.) and its foundational roots in
applied mathematics
(e.g.
classical and wave mechanics, covariant differentiation, etc.)