Introducing computational fluid dynamics (CFD) into undergraduate teaching of fluid mechanics is easily justified by the recent explosion in general access to high-quality commercial software. However, the ready availability of powerful CFD software also has its dangers from a pedagogical viewpoint if students are simply encouraged to tackle real problems without understanding the validity and limitations of these tools. The objectives of the Newcastle approach are to emphasize the underlying physical and mathematical concepts which will underpin CFD as commercial software continues to develop in the future. This emphasis has had a significant (and possibly controversial) impact on the choices adopted for applications, solution methods and teaching techniques, including the use of software. Inevitably the sheer breadth and multi-disciplinary nature of the subject means that great selectivity has had to be applied to topics addressed in a general-purpose undergraduate course.