“Intro to linear algebra.” 200-level. Vectors are (x,y,z), more or less. Class includes math, engineering, science, and business majors. 200-level makes it nominally a second-year course but lots of first-year students will take it. Required course for many different majors.
“Applied linear algebra.” 300-level. Vectors are finite. Eigenvalues, linear transformations, determinants, matrix algebra, factorization. Touches on numerical methods but doesn’t spend much time on them. Students were mostly math, with some physics and electrical engineers mixed in.
“Advanced linear algebra.” Series of two 400-level / 500-level courses. Almost exclusively math majors and math grad students. Algebraic topology, tensor spaces, exterior algebra, spectral theory, differential forms.
There were also numerical methods courses—one in the math department and one in the CS department.
From what I’ve seen, the year 2 course is great for graphics programming, game development, that sort of thing. It’s not enough for the tasks that require more serious linear algebra, when you’re working with systems of linear equations, large matrices, etc. These “big” linear algebra problems come up a lot in fields like physics simulation, finance, and machine learning / AI.
I’ve done some hobby work in graphics and game development, and I’ve done some professional work in physics simulation. The kind of linear algebra you use in physics simulation is a different beast.