[FR] Calculus III: Functions of multivariables and vectors

So this year I am taking four courses in high school and one course at the community college. This special part-time enrollment in a college class is a unique experience that I am happy to take with me to university next year.  I have taken several college courses before, but this is the first time I am taking a course during the academic school year.

The class is Calculus III (third semester of calculus, if that wasn't obvious) and it's similar to Calculus I (single variable calculus) with conceptual topics except instead of having a single variable, there are multiple variables.

What does this exactly mean?
The question may be difficult to answer depending on the amount of mathematics experience you have. For those with an Algebra II background (maybe even Algebra I), the function f with respect to x is represented f(x).

This means, for every one input x, there is a respective output, usually y. The dependent variable is responsive to only one independent variable. A simple x, y chart can numerically represent this concept and a graph can visually represent it.

For a function of two variables, a single output (now called z) responds to two independent variables x and y. Instead of f(x), the two variable analog represents a function f with respect to x and y as f(x, y).

Note that the letter f only represents the name of the function. The function can be named any letter (or symbol for that matter), but by convention generic functions are usually named f, g, and h.
For word problems, it may be logical to say the function A represents Area with height h and width w. So f(x, y) becomes A(h, w). This clarifies both clarifies the dependent and independent variables.

So if Calc I finds tangents, derivatives, and integrals in two dimensions, my class Calc III finds tangents, derivatives, and integrals in three dimensions. Instead of finding the area under a 2-space graph, we get to find the area under a 3-space curve. It is quite an interesting class.