Added description of PDE
"\\end{pmatrix}\n",
"$$\n",
"\n",
- "## Partial Differential Equations"
+ "## Partial Differential Equations\n",
+ "\n",
+ "A partial differential equation (PDE) is a differential equation that contains multiple independent variables. ODEs can be seen as a special case of PDEs. A partial differential equation of $u(x_1 \\ldots x_n)$ with $n$ independent variables takes the form:\n",
+ "\n",
+ "$$\n",
+ "F(x_1,\\ldots x_n; u,\\frac{\\partial u}{\\partial x_1},\\ldots \\frac{\\partial u}{\\partial x_n};\\frac{\\partial^2 u}{\\partial x_1 \\partial x_1},\\ldots \\frac{\\partial^2 u}{\\partial x_1 \\partial x_n};\\ldots)=0.\n",
+ "$$\n",
+ "\n",
+ "Similar as PDE, a general solution of a PDE contains arbitrary independent constants of integration. A particular solution is derived from the general solution by setting the constants to particular values. To fix to a particular solution, we need to impose initial value conditions and boundary value conoditions as well."
]
}
],
