- We're wrapping up week 15.
- Today we continue with some three-dimensional and geometric
content: vectors.
- Details on the final exam are starting to clarify:
- We're going to hold it at the time slot for the TR classes starting at 1:40, which is Thursday, 5/6, 12:20-2:20.
- You may be able to take it at the time of Prof. Wilkinson's section (Tuesday 5/4, 10:10), if that works out better for you. Let me know if that's an issue we need to pursue.
- You will be allowed a page of notes and a calculator.
Vectors possess two quantities: length and direction (or orientation). We usually think of them as arrows. A physical arrow is always point in a direction (but its direction changes based on how you're holding it -- that makes is orientation a function of time, say!). It's length usually doesn't vary.
- Materials:
- Vectors (.nb)
- Vectors (.pdf)
- Long talks you through vectors.
- Equation of the cardiod: $r(\theta)=1-\cos(\theta)$
- Area of the cardiod: $A=\frac{1}{2}\int_{0}^{2\pi}(1-\cos(\theta))^2\ d\theta = \frac{3\pi}{2}\approx 4.71$
- Length of the cardiod: $L=\int_{0}^{2\pi}\sqrt{(1-\cos(\theta))^2+(\sin(\theta))^2}\ d\theta = 8$