Lecture 1, Thurs, Sept. 23: Sections 1.1, the
beginning of 2.1 and 2.2
Here's a picture of the plane we graphed at the end of
class.
Lecture 2, Tues, Sept. 28: Sections 2.1, 2.2, and
the beginning of section 2.3 (review limits of functions of one variable!)
Here's another picture of
the plane we graphed. Notice its level curves are drawn in the x-y plane,
and when they are moved to the "right" height (z = c), they are all on the
surface of the plane.
Here's a graph of
the function with a dip in the middle of the surface. And here's the contour diagram (the plot of the level curves
in the x-y plane) of this surface.
Lecture 3, Thurs, Sept
30: We finished 2.3 and the first half of 2.4 Here's a picture of the function we proved had no limit.
at (0,0).
Lecture 4, Tues, Oct. 5: We went back to
Chapter 1 and covered Sections 1.3 and 1.5 (dot and cross products). We
used these to find parametric equations of lines in R^3 and also equations
of planes in R^3. Finally, we wrote down the equation of a tangent plane
to a surface z = f(x,y) at a point.
Lecture 5, Thurs,
Oct. 7: We finished linear approximations (Section 2.4) and covered some
product rules and the chain rule (Section 2.6).
Lecture
6, Tues. Oct. 12: We covered section 2.7 on gradients and directional
derivatives.
Lecture 7, Thurs. Oct. 14: Sections 4.1
(higher derivatives), 4.2 (second-order Taylor approximations), and 4.3
(critical points and the second derivative test).
See the pictures of the linear and quadratic approximations
for the function f(x,y)=sin(x+y)+cos(x-3y).
Lecture 8,
Tues., Oct. 19: We did examples of classifying critical points (using the
second derivative test) and did examples of finding the absolute minimum
and maximum of a function.
Lecture 9, Thurs., Oct. 21: We
covered 4.6 and 4.7 (the divergence and curl of vector fields, and
implicit differentiation).
Lecture 10, Tues., Oct. 26: We
covered most of sections 2.5, 3.1, 3.2 on parametric representations of
curves, and their velocity, acceleration, and tangent lines.
Lecture 11, Tues., Nov. 2: We reviewed curves, and covered 3.3
(length and arclength of curves), the definitions of "closed" and "simple"
from Chapter 5.1, and the definition of path integral from 5.2.
Lecture 12, Thurs., Nov. 4:
We finished 5.2, and started the path integrals of vector-valued
functions.
Lecture 13, Tues., Nov. 9: We finished 5.3, and most of 5.4.
Lecture 14, Tues., Nov. 16: We finished 5.4 and covered sections
6.1, 6.2 on double integrals and switching the order of integration on
various regions.
Lecture 15, Thurs., Nov. 18: We discussed changing variables (from
(x,y) to (u,v)) in a double integral.
Lecture 16, Tues., Nov. 23: We briefly discussed triple integrals
and reviewed change of variables, and then introduced the definition of
surface integrals.
Lecture 17, Tues., Nov. 30: Section 8.1: Green's Thorem.
Lecture 18, Thurs., Dec. 2: Review.