Block 2: Functions In Calculus Revisited Part 1, Professor Gross discussed the
calculus of a single real variable in which the domain of a function was a subset of the real numbers. Geometrically
speaking, the domain of a function was a subset of the xaxis. In this block he generalizes the domain as being a subset of
either the twodimensional xyplane and/or the threedimensional xyzspace. In the language of vectors, in this block a function
maps 2 and 3 dimensional vectors into the set of real numbers. He then uses these functions to show how we compute the velocity
and acceleration of an object moving in space.

Block 3: Real Valued Functions of Several Real
Variables In this block
Professor Gross uses the "game of mathematics" concept to develop an analytical way to extend the domain of a function
to beyond 3 dimensions. In particular, he shows how by using vector arithmetic, the rules of arithmetic that were used in
developing the calculus of a single variable turn out to be the same that we use to develop the calculus of several variables.
This leads to a discussion of how we replace the concept of slope in the 2 and 3dimensional calculus by such concepts as
the directional derivative when dealing with more than 3 dimensions.

Block 4: Matrix Algebra Block 4 extends the concept of inverse functions to
the case where y = f(x) with y = (y_{1}, y_{2}, ..., y_{n}) and x = (x_{1}, x_{2}, ..., x_{n}). In more userfriendly
terms this block asks us to determine when and how the system of equations that expresses y_{1}, y_{2}, ... and y_{n }as
functions of x_{1}, x_{2}, and x_{n} can be "inverted" to express
x_{1}, x_{2}, ... and x_{n }as functions of y_{1},
y_{2}, ... and y_{n}. This motivates the study of matrix algebra since the process of inverting an n x n square
matrix is used to show how we decide whether a function f(x_{1},
x_{2}, ..., x_{n}) has an inverse and how we find the inverse function if it exists.
