'fin diff'

Author: DPotoyan

math/note05.ipynb

@@ -168,7 +168,7 @@
     "\n",
     "$$ \\frac{d\\psi}{dx} \\approx \\frac{\\psi(x_{i+1}) - \\psi(x_{i-1})}{2h} $$\n",
     "\n",
-    "This operation can be represented by a matrix. For $n = 5$ grid points, with improved boundary handling, the first derivative matrix $D_1$ using the centered difference method looks like:\n",
+    "- This operation can be represented by a matrix. For $n = 5$ grid points, with improved boundary handling, the first derivative matrix $D_1$ using the centered difference method looks like:\n",
     "\n",
     "$$\n",
     "D_1 = \\frac{1}{2h}\n",
@@ -179,7 +179,9 @@
     "0 & 0 & -1 & 0 & 1 \\\\\n",
     "0 & 0 & 1 & -4 & 3\n",
     "\\end{pmatrix}\n",
-    "$$\n"
+    "$$\n",
+    "\n",
+    "- The coefficients $-3,4,-1$ come from applying a Taylor series expansion to derive a higher-order accurate one-sided difference approximation for the derivative at the boundary point. "
    ]
   },
   {