From introduction

"Pure mathematics" and "applied mathematics" essentially

form an organic unit. In spite of this, however, a narrow

specialization has developed in each of these two fields. In

consequence, there exists an unfortunate tendency on the part

of the representatives of on field to disregard the endeavers

of those of the other. The "pure" mathematician sometimes

considers a difficult problem as solved if he is able to

demonstrate that a logical contradiction follows from the

assumption that the problem does not possess a solution.

Difficult as such a logical achievement may be in certain cases,

the claim to have "solved" the problem in this manner will not

impress the engineer. The latter is not so much interested in

as "existence" proof as he is in the actual construction and

mastering the the explicit solution. On the other hand, those

who are interested solely in practical results and applications

are not always satisfied merely with "routine recipes". For

them a deeper penetration into the mathematical background is

indispensible if they would become independent of rigid

patterns.

This course will emphasize mathematical methods which are

connected with important types of applied problems. The

isolation of the essential mathematical features from the

physical features of a given problem often exhibits the core of

the problem and shows that apparently different and independent

phenomena may have identical underlying structures. For

example, the mathematical formulation of mechanical vibration

problems on the one hand and of electrical vibration problems

on the other exposes certain structural similarities between

the two fields. The tendency must be to consider such a

diagnostic procedure as a basis for a therapeutic treatment,

that is, for the actual mastering of the solution.

The main topics of this course will be (1) the mathematical

theory of vibrations, with a view toward discussing questions

of stability and equilibrium, and (2) the theory of wave

propagation.........