I have a reason to believe that Euler introduced the complex potential in his Continuation des recherches sur la theorie du mouvement does fluides, published in 1757. However, I am having hard time recognizing where it appears. The relevant place seems to be here:

enter image description here

After establishing that $(u-iv)(dx+idy)$ and $(u+iv)(dx-idy)$ are integrable, he introduces functions $\phi$ and $\psi$. The problem is I am not sure what $\phi:(x+yi)$ means. Normally, I would expect the expression to involve some kind of derivative, such as $$ (u-iv)(dx+idy) = d\phi + id\psi. $$

I am hoping somebody could explain what is going on here.

If you need, Euler continues on the following page as:

enter image description here




Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.