Definitions and a few problems from complex analysis.
| Front | What does it mean for a complex function f(z) to be differentiable at \(z = z_0\). |
| Back | Let \(D \subseteq \mathbb{C}, f: D \to \mathbb{C}, z_0 \in D\).if \(f'(z_0) := \lim_{z \to z_0} \frac{f(z) -f(z_0)}{z-z_0}\) exists, then f is differentiable at \(z_0\). |
| Front | What are harmonic conjugates? |
| Back | If u and v are harmonic such that \(f(x+iy) = u(x,y) + iv(x,y)\) is differentiable, then u,v are harmonic conjugates |
| Front | What is a 2 dimensional Laplace equation? |
| Back | Let \(U \subseteq \mathbb{R}^2\) be an open set, \(u: U \to \mathbb{R}\)\(\frac{\partial^2}{\partial x^2} u + \frac{\partial^2}{\partial y^2}u = 0\) |