I haven't studied multivariable calculus yet but I have a question that bothers me. Let $F$ be a function $\mathbb{R}^2 \to \mathbb{R}$. Imagine that we rotate the co-ordinate axis by an angle $\theta$. I think the shape of the function should change. How should this function change if we make a rotation of the co-ordinate axis by some angle?
What is the effect of axis rotation on functions defined on $\mathbb{R}^{2}$
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multivariable-calculus
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0Do you mean to rotate in the plane of inputs $R^2$? If so this will only rotate the entire graph of $F$. If you want to rotate the entire $R^3$ in which the graph lies, the rotation may not even give the graph of a function. – 2012-11-04
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0Yes, I mean to rotate the domain . How can we express the new function in terms of the old function and the angle $\theta$? – 2012-11-05