This book arose from a course of lectures given during the
academic year 1954/55 at the Mathematical Centre, Amsterdam,
repeated in 1956/57 in a course at Eindhoven, organized by the
same institution. Its purpose is to teach asymptotic methods by
explaining a number of examples in every detail, so as to suit
beginners who seriously want to acquire some technique in attacking
asymptotic problems.
Although asymptotics is by no means a new field, only in recent
times have special courses and books been devoted to it. The
reason may be that today university courses in analysis are
condensed in favour of modern mathematics. The effect is that analytic
techniques are not so widespread as they used to be. On the other
hand there are so many questions of an asymptotic nature both in pure
and applied mathematics, that we cannot afford to neglect the
subject. Therefore it seems desirable to give a separate training in
asymptotics to those who have only a general knowledge of analysis.