I'll add that in the US at least, most students don't start learning QM in an upper-division undergraduate course using a textbook like Griffiths. They get their first exposure to QM in an "introductory modern physics course" that comes after the usual two-semester first-year introductory course in classical mechanics and electromagnetism. Typical textbooks are by Krane; Tipler; Beiser; Taylor/Zafiratos/Dubson; Ohanian. You can find them on Amazon using searches like "krane modern physics"
These books typically assume only that the student knows basic differential and intergral calculus, and introduce or review partial derivatives, basic stuff about complex numbers, and the concepts of orthogonality etc. from linear algebra, as needed. They usually cover solutions of Schödinger's equation for the "particle in a box", barrier penetration ("tunneling"), the simple harmonic oscillator, and at least an outline of the solution for the hydrogen atom. I taught a course like this for many years, to students who had usually completed at most only the first two semesters of calculus. After that course, they took a "real" QM course using Griffiths or a similar book.
