1. Parametric Equations HW: 11.1; 3,22

2. Why do we need parametric equations? Consider the flight of a golf ball…the motion consists of two independent parts (Galileo’s “big” insight): Falling motion or Galileo’s Law of falling bodies in the vertical (y) direction Uniform translational motion in the horizontal (x) direction

3. “In Math”… Vertical motion: Horizontal motion: “t” is the parameter

4. What path does a golf ball follow? But how are x and y related to each other?

5. A famous historical example … the Cycloid What path does a point on the rim of a circle trace as the circle rolls at a constant rate without slipping?

6. So, why do we need parametric equations? By finding the suitable parameterization you can sometimes express relationships between variables that would otherwise be very difficult to do.

7. Next lecture… Applying ideas of calculus to parametric equations Read 11.2 HW: 3, 15