The subject matter of this book formed the substance of a
mathematical se am which was worked by many of the great
mathematicians of the last century. The mining metaphor is here
very appropriate, for the analytical tools perfected by Cauchy
permitted the mathematical argument to penetra te to unprecedented
depths over a restricted region of its domain and enabled
mathematicians like Abel, Jacobi, and Weierstrass to uncover a
treasurehouse of results whose variety, aesthetic appeal, and
capacity for arousing our astonishment have not since been equaled
by research in any other area. But the circumstance that this
theory can be applied to solve problems arising in many departments
of science and engineering graces the topic with an additional aura
and provides a powerful argument for including it in university
courses for students who are expected to use mathematics as a tool
for technological investigations in later life. Unfortunately,
since the status of university staff is almost wholly determined by
their effectiveness as research workers rather than as teachers,
the content of undergraduate courses tends to reflect those
academic research topics which are currently popular and bears
little relationship to the future needs of students who are
themselves not destined to become university teachers. Thus, having
been comprehensively explored in the last century and being
undoubtedly difficult .
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