Additional materials and handouts
Studying and doing mathematics
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.
Exam review materials
First exam review (includes practice problems)
Second exam review (includes practice problems)
Final exam review (includes practice problems)
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)