I have started compiling some review materials for math 32A and 32AH for this quarter. They consist of

I will post solutions to the exercises before the review session on Thursday. As always, let me know in the comments below if anything is unclear or incorrect.

Update I have posted the solutions to the practice problems. Also, a student pointed out a typo in statement of the final problem in the review. Spherical coordinates should be given by

$$

x = \rho \cos \theta \sin \varphi, \quad y = \rho \sin \theta \sin \varphi, \quad z = \rho \cos \varphi.

$$

These changes have been made in the version of the problems and solutions online.

Update 2 There was a mistake in the solution of problem 10 involving curvature. This has (hopefully) been fixed.