Additional materials and handouts

Materials supplementing the lectures

  • Plotting vectors in 3 dimensions (you can also compute the sum, difference, and the cross product)

  • Here is a site that lets you play with quadric surfaces. Here is another one.

  • Here is a site that lets you graph general surfaces z=f(x,y).

  • Here is an app you can download to play with surfaces in augmented reality!

  • Here is an applet that lets you draw some contour maps. And here is one that lets you look at all the level curves.

  • Here is a site that lets you draw parametric curves.

  • Here is an applet that lets you visualize partial derivatives.

  • Here is an applet that lets you visualize the gradient vector.

  • Here is an applet that lets you visualize directional derivatives.

  • Here is another page that lets you play around with the gradient vector and directional derivative on a mountain.

  • Here is an applet that lets you plot vector fields in the plane. And here is one for vector fields in 3-space.

  • Here is an applet that lets you visualize Green's Theorem.

  • Here are pages that talk about the divergence and curl of a vector field. Here is a video with some motivation for studying divergence and curl.

  • Here is an applet that lets you play around with curl, divergence, and work done by a vector field.

  • Summary of line and surface integration

Exam review materials

Zoom lecture videos and notes

  • Section 12.2 video and notes (watch before Friday, September 4 class)

  • Section 12.3 video and notes (watch before Friday, September 4 class)

  • Section 12.5 video and notes (watch before Tuesday, September 8 class)

  • Section 12.6 video and notes (watch before Tuesday, September 8 class)

  • Section 13.3 video and notes (watch before Friday, September 11 class)

  • Section 14.3 video and notes (watch before Tuesday, September 15 class)

  • Section 14.6 video and notes (watch before Friday, September 18 class)

  • Section 15.1 video and notes (watch before Tuesday, September 22 class)

  • Section 15.3 video and notes (this was a synchronous zoom class on Tuesday, September 22 with everyone attending)

  • Section 15.6 video and notes (watch before Tuesday, September 29 class)

  • Section 16.3 video and notes (watch before Friday, October 9 class)