In this video we review some definitions and give an example of long division using rational functions. The whole point is that we can write any rational function as the sum of a polynomial and a "proper rational function" meaning the numerator has lower degree than the denominator. It is these types of rational functions that we are able to apply partial fractions to.
This is a continuation of change of variables introduction part 1. In this video we give a more useful example of finding a change of variables of a rectangle which produces a given more complicated shape (namely a parallelogram).
In this video we go back forth between curves described by polar coordinates and Cartesian coordinates. We also sketch a few curves given in polar coordinates.
This first example is the easiest case. We have two distinct linear factors in the bottom and so the rational function splits up nicely into two pieces that we can integrate.
Goes over basic examples and ideas involved in functions of several variables. Includes a discussion of contour plots and graphs of functions of two variables.
