I was looking through a calculus book doing some of the practice problems where I was asked to calculate the curl of a few functions. One of them got me thinking, is there a function whose curl is itself? Much like how [itex]e^{x}[/itex] is it's own derivative, is there a vector field that is it's own curl?(adsbygoogle = window.adsbygoogle || []).push({});

[tex]∇×F = F[/tex]

Are there any non-zero general solutions to this problem? This will expand to a system of 3 linear PDE's with 3 unknowns. The problem is, I'm new to PDE's and don't know how to solve them. I am familiar with ODE's to some extent, and I understand that the goal is to simplify a PDE into an ODE. So my question... how would I go about solving this problem? Do you know any good online references that would teach me? Thank you for your time.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Curl F = F, solve for F (PDE)

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**