- Hour exam 1
- Monday (Oct. 5)
- Covers material up through Oct. 2 (this Friday), e.g., 3D coordinates, surfaces, vectors & operations on them, lines & planes, vector-valued functions & their derivatives & integrals, arc length, curvature
- 4 - 6 short-answer questions, similar to problem sets
- Full class period
- Open reference materials (book, notes, computer); closed person
- Section 13.3
- Arc length as integrals — anti-climactic because it is really just extending ideas about arc length with 2D parametric equations to 3 equations
- “Direction” on curves?
- Mapping between t and distance parameterizations?
- Example
- r(t) = ⟨ t2-1, 3t2, -t2 ⟩
- What is s(t) (arc length parameter for r)?
- For Friday: finish working out s(t)
- What is s(t) (arc length parameter for r)?
- r(t) = ⟨ t2-1, 3t2, -t2 ⟩
- Finish arc length, including numeric integration (bring laptop)
- Ideally, curvature too