Backed-up Laplace PDE equation

docs/assets/LaplacePDE.tex

@@ -0,0 +1,8 @@
+\begin{align*}
+    \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} &= 0 \qquad \qquad \qquad \text{in } (0,1)\times (0,1) \\
+    \frac{\partial u}{\partial y}(x,0) &= 0 \qquad \qquad \qquad \text{on } [0,1]\times \{0\}    \text{  (South)} \\
+    u(x,1) &= \sin(\pi x) \qquad \quad \,\, \text{on } [0,1]\times \{1\} \text{  (North)}\\
+    u(0,y) &= 0 \qquad \qquad \qquad \text{on } \{0\}\times (0,1)  \text{  (East)}\\
+    u(1,y) &= 0 \qquad \qquad \qquad \text{on } \{1\}\times (0,1)  \text{  (West)}
+\end{align*}
+