Unit 11 – Chapter 11
Module Overview
In this chapter, we start examining the effect of having an independent variable determine two (and, in the next chapter, three) dependent coordinates. The most common applications are those in which we use the parameter of time to describe physical motion through the plane and through space.
Learning Outcomes
- Section 11.1: With this section we begin to expand calculus beyond some of the boundaries we had faced so far. We no longer look at the independent variable as a part of the graph of a function and instead allow it to be a parameter that determines both the x and y coordinates. This opens up a tremendous number of applications.
- Section 11.2: The most important single type of parametric equations is polar coordinates. These are a very natural idea – we describe the position of an object by giving a heading and a distance (our definition of a vector), rather than giving x and y coordinates (which is how we end up writing vectors).
- Section 11.3: In this section we expand on our ideas from 11.2. With polar coordinates defined, we find that we can do quite a bit of useful math with them, including a definition of area that we could not get with other parametirc equations.
- Section 11.4: A bit of a geometry interlude. In this short section we look at the most important types of non-polynomial curves (there is an intersection here, as parabolae end up being exactly the quadratic polynomials) and learn a bit about their origin.
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