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.)