This book is an account of lectures that I gave at AIMS (the African Institute of Mathematical Sciences) in 2008, which were developed from two earlier courses I had given there in 2004 and 2006. I did not set out to write a textbook but rather to present a diary, summarising and reviewing what I had tried to convey to the students in the hour or two immediately preceding writing. This reflects the fact that lectures at AIMS are dynamic, interactive sessions and I had prepared little by way of formal lecture notes in advance. To be sure, there was some didactic delivery of ideas, but that lecturing activity was interspersed with problem-solving activities and many, many questions from students so that the educational process was much more of a conversation than is typical of most university courses I have given. Having now put this material in writing, I hope that it might interest and inspire students and teachers alike but will not constrain or encourage future lecturers at AIMS or elsewhere to teach rigidly from the book.

Where, in the course of writing, I discovered some small point that I had omitted to mention or some additional clarification or illustration that I felt would be helpful, I allowed myself to include it. Other than that, I have made no attempt to expand upon what I taught or to provide a comprehensive introduction to fluid dynamics. A student interested in pursuing the ideas further should consult any of the many excellent texts that exist in this subject, a few of which are described in the Bibliography.

In my view, fluid dynamics as a discipline sits squarely between physics and mathematics. It is important to understand the physical interactions involved well enough to codify them within mathematical equations, and to have sufficient mathematical insight to know whether the equations are likely to be manageable. The equations must then be solved, often by making approximations with enough physical insight to know whether the important interactions have been retained, and with enough mathematical rigour to have confidence in the resulting predictions. And finally, the mathematical solution must be interpreted in a way that sheds light on the physical problem being studied.