Advanced Methods In Applied Mathematics - Richard Courant
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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
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

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No. of Pages 318