Lecture 7, Wednesday, 9/10/08:
Section 11.4: Curvature
Topics
- Arclength function s(t)
- Arclength parameterization of curve
- Unit tangent vector T(t)
- Curvature K: Geometric meaning and computational formulas:
(a) tangent vector formula (4.4); (b) cross product formula (4.7).
- Curvature of a circe of radius R
- Osculating circle (the book discusses this in the following section
(11.5), on p. 898)
Read
Section 11.4. You should memorize the two formulas for the curvature
mentioned above (which apply to general parameterized curves),
but not the formula for a plane curve y=f(x) given in (4.8), or (4.3)
(which is mainly of theoretical interest).
Homework
Section 11.4: 1, 3, 5, 7, 17,
29.
Solutions.
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Last modified Mon 22 Sep 2008 02:17:37 PM CDT