The curl in 2D is commenly written as $\text{curl}_{2D}(u) = \frac{\partial u_2}{\partial x_1} - \frac{\partial u_1}{\partial x_2}$. It is often described as thinking of 3D field with the thrid component being zero. Then the curl will have only one non-zero component, and this scalar value is then used as 2D curl.
As I am writing a thesis where I heavily use this "definition" of the 2D curl. I would like to cite a textbook (or a paper) because I did not make this "definition". So my question is, do you know any textbook (or paper) containing this description/definition?
(Note: I do not know which would be the correct tag for this question, so I kindly ask you to correct the tag if wrong.)