Observation 3 - Starting 14.2

• They need to read 14.3 by Friday.
• I really need to ask Brussel:
  1. If I can present my second marketing pitch next week
  2. What platform of communication he'd prefer.

Reviewing 12.6 and Similar

They first look at the level surfaces of $x+3y-2z$:

• Some didn't really know that it was a plane, as some just thought it was from the group of 12.6 surfaces.
• They should know this from their previous year of Calc
• Brussel saw this flaw and reviewed:
  • Ellipsoid
  • Hyperboloid
  • Hyperbolic Paraboloid
  • Paraboloid
  • ... (it's funny since we reviewed these in workshop yesterday)
• He quickly talked about hints to the 12.6.21 - 28
• However it seems that it was a bit fast. I think having them do it in Geogebra and seeing the shapes themselves is good. I do think they need to do it with the algebra.

Reviewing 14.1

They looked at 14.1.56, plotting $V(x,y)=\frac{c}{\sqrt{r^2-x^2-y^2}}$ as a contour diagram.

• They were able to gripe that $r^2-x^2-y^2>0$, so then $r^2>x^2+y^2$, so defined in a circle of radius $r$.
• They definitely need to parse the range from the graph, to extrapolate to draw $kc/r$ level curves. This is a weak point of theirs.

They actually did way more of quadric surfaces again, trying to identify $(x/3{)}^2+(y/2{)}^2+z^2=1$.

• Someone got that it was an ellipsoid.
• Drawing may be a sore point. One thing is to scale the axis for them.

They'll start Partial Derivatives (14.3) tomorrow.