3. Cauchy-Riemann Equations

Harmonic Functions — Quiz

Test your understanding of harmonic functions with 5 practice questions.

Practice Questions

Question 1

Which condition must a twice continuously differentiable function $u(x,y)$ satisfy in order to be harmonic?

Question 2

For $u(x,y)=x^2-y^2$, what is $u_{xx}+u_{yy}$?

Question 3

What is the real part of $f(z)=z^2$ when $z=x+iy$?

Question 4

A harmonic conjugate of $u(x,y)=x^2-y^2$ is which function?

Question 5

Which function is harmonic on $\mathbb{R}^2$?