Vectors and matrices and more vectors and more matrices. This course (or often Calc III) is usually the first in which you learn to truly do mathematics in multiple dimensions--two, three, or more! But the mathematics of six dimensions is very complicated, and here you simplify by studying the higher-dimensional analogues of linear functions (mx+b) only. So forget parabolas, trig functions, exponentials, and all the other functions which made matters complicated, and focus on functions that Do not curve. There is a great deal to be said even about such a simple class of functions when you say it in twelve dimensions!

When passing from one dimension (mx+b) to several, the numbers x get replaced with vectors. Matrices are the replacement for m. The simple multiplication of m*x becomes matrix*vector multiplication, which you'll have to learn how to do!