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Given any vector field , how do i either: calculate the rotation using vector calculus definition, use the differential forms definition of rotation and use differential geometry to show at leat that the vector field is integrable( has zero rotation). Example : 1.constant gravitational vector field g 

               2. A vector field that is written in component form: v=3y in epsilon direction + 2x in y direction

They key is , no mater what vector field i have , can i interpret in a way to calculate the rotation without any coordinates?

Tyson
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  • I am confused by what you mean by vector calculus definitoin: If you are using the curl, this is a coordinate dependent notion. – operatorerror Nov 18 '17 at 21:46
  • If youre confused about vector calculus definition, the alternitive is differential forms definition. Vector calculus also has a coordinate independent definition. – Tyson Nov 25 '17 at 12:07

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