Can someone help me solve these problems

  • Thread starter shankarvn
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In summary, the conversation is about a mechanical engineering graduate seeking help with solving problems from a textbook on differential forms by Manfredo P Do Carmo. They have attached the file and are specifically looking for help with problem 1, which involves orientation on charts, problem 2, which deals with the intersection of charts, and problem 3, which requires the use of the uniqueness theorem for initial value problems of differential equations.
  • #1
shankarvn
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Hi everyone

I am a mechanical engg graduate. Can someone help me solve these problems?
This are problems from our textbook on differential forms by manfredo P Do carmo. I have attached the file.
Thanks
 

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  • #2
shankarvn said:
Hi everyone

I am a mechanical engg graduate. Can someone help me solve these problems?
This are problems from our textbook on differential forms by manfredo P Do carmo. I have attached the file.
Thanks
For 1, note that the orientation on each chart has to agree on the connected intersection, so it must be either positive or either negative throughout.

For 2, show that the intersection of the charts is connected (it actually is the equator).

For 3, use the uniqueness theorem for initial value problems of differential equations.
 

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