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math105-s22:hw:hw12 [2022/04/16 09:23] pzhou created |
math105-s22:hw:hw12 [2022/04/16 09:24] (current) pzhou |
====== HW 12 ====== | ====== HW 12 ====== |
1. Can you verify explicitly that any closed differential 2-form in $\R^3$ is exact? | - Following Thursday's class, can you verify explicitly that any closed differential 2-form in $\R^3$ is exact? |
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2. (optional) read about Brouer's fixed point theorem in Pugh, and try Pugh Exercise 71, [[https://en.wikipedia.org/wiki/Hairy_ball_theorem | hairy ball theorem]]. | - (optional) read about Brouer's fixed point theorem in Pugh, and try Pugh Exercise 71, [[https://en.wikipedia.org/wiki/Hairy_ball_theorem | hairy ball theorem]]. |
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