(al Consider the 1-form w=-y dx + xdy. Sketch the corresponding vector field. Then compute the "curl" 2-form dw. What feature of your sketch is captured by dw? ( Consider the vector field F = zzi - y²j + 2x²yk. Define curl(F) in terms of the derivative of a 1-form and then calculate curl(F). (c) Consider the 0-form w = ²y2³ and the vector field F = rzi-y²j+2r²yk. Determine grad(w), div(F), curl(F), div(wF), curl(wF). [See 7.34]

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