Designing a mathematics course for 1st year chemistry students
At least in the US, most undergraduate chemistry curricula do not go deep enough into the math of QM that you need to spend a great deal of time on it. Students that do take more advanced QM classes can learn the math at that time. I also am not sure it's safe to assume that all incoming students at that level have a good understanding of 1D calculus, though most will have had some exposure.
With that in mind, here are topics that I'd include (not in any specific order), structured around the relevant applications:

basic calculus review of integration and differentiation in 1D - main intro level application is chemical kinetics. Also applies to intro quantum.

setting up and solving systems of equations, especially including iterative solving methods - intro level application is solving systems of multiple equilibria by mass and charge balance

a module on statistics with a focus on dealing with experimental error and error propagation. Include methods of curve fitting and associated pitfalls. - applies to lab component of curriculum. Probably one of the more commonly overlooked aspects of math in chemistry

Fourier transform and other techniques involved in spectroscopy

Basics of symmetry operations and group theory