Our department teaches two very large first-year "Mathematical Methods" courses (600-ish students) to Engineering students. The syllabus is dictated by their (future) needs and covers a huge array of topics, but none to any great depth.
For resourcing reasons, we cannot put on a separate course for the 10-15% of students who might go on to study Maths or Physics, but we feel that a breakneck tour through a huge number of mathematical methods is not an ideal start for these students.
We are exploring methods of adding (optional) depth to this course to better serve this small subset of the students. So far we've tried having optional "explore by yourself" sections in the weekly tutorial sheets, and we've tried having out-of-class optional "enrichment lectures", but neither of these has worked really well.
So my question is: given the constraints outlined above, what are possible methods of adding optional mathematical depth to an Engineering maths course to better serve future Maths students?
I know that this is rather vague and wishy-washy, but I'm really after anecdotal experiences from people who have tried this sort of thing.