In the summer of 1941 Brown University undertook a Program of Advanced
Instruction and Research in Mechanics. This in fact was the precursor to
the present day Division of Applied Mathematics. Certainly an
outstanding feature of this program must have been the lectures in Fluid
Dynamics by Professor Friedrichs and the late Professor von Mises. Their
notes were prepared in mimeograph form and given a wide distribution at
that time. Since their appearance these lectures have had a strong
influence on teaching and research in the subject. As the reader soon
learns the notes have lost none of their vitality over the years. Indeed
in certain instances only in the last few years has the -field caught up
with the ideas developed in the course of these lectures. Many ideas of
value are still to be found in these notes and the Editors are most
happy to be able to include this volume in the series. The corrections
which have accumulated over the years have been incorporated, and in
addition an index has been added. With these exceptions all desire to
revise has been resisted. Also in this connection we are very grateful
to Dr. T. H. Chong for carefully overseeing the preparation of the
present manuscript.