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Vector-fields are vector valued functions which define a vector at each point in space. Examples of the vector field include the electric field and the velocity of a fluid.

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Transformation law of vector fields on $\mathbb{R}^n$

So suppose we have a function $F$ from $\mathbb R^2$ to $\mathbb R^2$ defined by $F(x,y) = (g(x,y),h(x,y))$ where $g$ and $h$ represent temperate and pressure respectively (the point is, they are both …