What Math Skills do Students Taking Physics Need to Have?
(the link to a pdf file is at the end of this short introduction)
And students need to know as well what math do they need to have in order to feel themselves comfortable when taking physics.
And the full set of such math skills comes from the full set of problems students need to be able to solve (actually or potentially) during (and after) the course.
BTW: it should be obvious that physics teachers should have at least the same set of math skills.
The rule of thumb for a science teacher: a teacher needs to know the material at least three grades above the material he/she teaches - but that is the minimum requirement.
And there are more on the pages of this blog.
The developed set of math problems (see the links below) is presented to students at the beginning of each course in the form of a laboratory exercise. Initially, it was handed out to students during the lab time, but eventually it was converted into a webassign.
Dr. Valentin Voroshilov
Education Advancement Professionals
The voices of my students
"The Backpack Full of Cash": pointing at a problem, not offering a solution
Essentials of Teaching Science