Our department, Scientific Computing, is highly interdisciplinary, and we get graduate students from very different backgrounds.
Here is a list of resources, I recommended incoming grad students to look at before they start.
These video lectures by Gilbert Strang and Cleve Moler present a quick summary of ODEs and major Linear Algebra topics.
In addition to a compiled language like C++/Fortran/Java, it is useful to know either Matlab or Python
This contains a set of extremely useful jupyter or iPython notebooks (PDF link if you don't have jupyter installed) which provide a gentle introduction to Python in Scientific Computing. It also includes several advanced topics (parallel programming, incorporating C and Fortran, version control etc.)