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.

Type: Video Links
Title	Author	Description
Parametric Equations \| Parametric Equations	Shai Cohen
Parametric Equations - Derivatives of Parametric Equations \| Parametric Equations - Derivatives of Parametric Equations	Shai Cohen
Tangent Lines Example \| Tangent Lines Example	Shai Cohen
Polar Coordinates \| Polar Coordinates	Shai Cohen
Polar Coordinates - 30d Relating Polar and Rectangular Coordinates \| Polar Coordinates - 30d Relating Polar and Rectangular Coordinates	Shai Cohen
Polar Coordinates - Graphing with Polar Coordinates \| Polar Coordinates - Graphing with Polar Coordinates	Shai Cohen
Polar Coordinates - Symmetry in Polar Graphs \| Polar Coordinates - Symmetry in Polar Graphs	Shai Cohen
Polar Coordinates Example - Finding Theta \| Polar Coordinates Example - Finding Theta	Shai Cohen
Polar Coordinates Example - Sprials \| Polar Coordinates Example - Sprials	Shai Cohen
Calculus in Polar Coordinates - Derivatives in Polar Coordinates \| Calculus in Polar Coordinates - Derivatives in Polar Coordinates	Shai Cohen
Calculus in Polar Coordinates - Area of Polar Graphs \| Calculus in Polar Coordinates - Area of Polar Graphs	Shai Cohen
Calculus in Polar Coordinates Example - Polar Derivatives \| Calculus in Polar Coordinates Example - Polar Derivatives	Shai Cohen
Calculus in Polar Coordinates Example - Horizontal Tangents \| Calculus in Polar Coordinates Example - Horizontal Tangents	Shai Cohen
Calculus in Polar Coordinates Example - Polar Area \| Calculus in Polar Coordinates Example - Polar Area	Shai Cohen
Calculus in Polar Coordinates Example - Polar Area Difficult \| Calculus in Polar Coordinates Example - Polar Area Difficult	Shai Cohen
Conic Sections \| Conic Sections	Shai Cohen