• Chapter 9 supplements (Stewart)
• Chapter 10 supplements (Stewart)

Week 4

9. Lecture: parametrization of surfaces Parametric surfaces

10. Lecture: functions and continuity Continuity

11. Lecture: partial derivatives

Week 3

6. Lecture: parametric curves Curve matching

7. Lecture: arc length and curvature Arc length example Feel for curvature Leave out reparametrization of curves. It is a more problematic topic.

8. Lecture: cylindrical and spherical coordinates Cylindrical coordinates An older exercice: Boston-Rome

Week 2

3. Lecture: Cross product, planes start Possible lesson plan third lecture Some questions An older in class exercice

4. Lecture: Lines, planes and distances Possible lesson plan forth lecture An inclass exercice

5. Lecture: Lines, planes and distances Possible lesson plan fifth lecture A reasonable matching exercicee Solutions A very difficult matching exercicee

Week 1

1. Lecture: Coordinates and Distances Possible lesson plan first lecture Completion of squares the lecture in 10 minutes [Movie] the lecture in 10 minutes [PDF]

2. Lecture: Vectors and Dot product Possible lesson plan second lecture Color the lecture in 10 minutes [Movie] the lecture in 10 minutes [PDF]

Questions and comments to knill@math.harvard.edu

Math21b | Math 21a | Fall 2009 | Department of Mathematics | Faculty of Art and Sciences | Harvard University