- Hour exam 1
- Monday
- Covers material up through today, e.g., 3D coordinates, surfaces,
vectors & operations on them, lines & planes, vector-valued
functions & their derivatives & integrals, arc length
- Chapters 12 + 13.1 - 13.3
- 4 - 6 short-answer questions, similar to problem sets
- Full class period
- Open reference materials (book, notes, computer); closed person
- r(t) = ⟨ t2-1, 3t2, -t2 ⟩
- What is s(t) (arc length parameter for r) relative to t = 0?
- v(t) = ⟨ 2t, 6t, -2t ⟩
- |v(t)| = 2√11 t
- Length of curve from t = 1 to t = 2? What about t = -1 to t = 1?
- Length from 1 to 2 = s(2) - s(1)
- From -1 to 1 distance = 0
- From -1 to 0 + from 0 to 1 = 2√11
- How can same length be different from itself? Because first calculation violates requirement that curve only trace its path once. Pay attention to the fine print in mathematics!
- How long is our snake?
- Integral of |v(t)| isn’t integrable symbolically
- …So use muPad or similar to do it numerically
- What is s(t) (arc length parameter for r) relative to t = 0?
- (After exam)
- Curvature of vector-valued functions
- Read section 13.4