Math 23b: Useful supplements

Here we will collect images, videos, and tools which I think are potentially useful.

Introduction to double integrals — Have a look at the images and movies here https://instruct.math.lsa.umich.edu/lecturedemos/ma215/docs/15_2/examples.html.

Double integration theory — I wrote you all a little supplemental note here: double_integral_theory

Spherical coordinates online tool visualizer:

https://mathinsight.org/spherical_coordinates

Practice midterm: Math 23b Practice Midterm

Practice Midterm solutions:

23b_practice_midterm_solutions_2-3

more_midterm_solutions

final_part_of_midterm_solutions

Practice Midterm: Errata

Practice Final

Practice Final Solutions