Cleanup for 07_differentiation

Author: mspieg

07_differentiation.ipynb

@@ -14,6 +14,13 @@
     "</table>"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -152,7 +159,7 @@
     "\n",
     "Where the Lagrange remainder term is\n",
     "\n",
-    "$$R_N(x) = (x - x_0)(x - x_1)\\cdots (x - x_{N})(x - x_{N+1}) \\frac{f^{(N+1)}(c)}{(N+1)!}$$"
+    "$$R_N(x) = (x - x_0)(x - x_1)\\cdots (x - x_{N}) \\frac{f^{(N+1)}(c)}{(N+1)!}$$"
    ]
   },
   {
@@ -504,7 +511,7 @@
     "\n",
     "From Lagrange's Theorem,  the remainder term looks like\n",
     "\n",
-    "$$R_N(x) = (x - x_0)(x - x_1)\\cdots (x - x_{N})(x - x_{N+1}) \\frac{f^{(N+1)}(c)}{(N+1)!}$$"
+    "$$R_N(x) = (x - x_0)(x - x_1)\\cdots (x - x_{N})) \\frac{f^{(N+1)}(c)}{(N+1)!}$$"
    ]
   },
   {
@@ -974,7 +981,7 @@
     "    f'(x_n) + R(x_n) = A f(x_{n+1}) + B f(x_n) + C f(x_{n-1})\n",
     "$$\n",
     "\n",
-    "where $R(x_n)$ is our error.  "
+    "where $R(x_n)$ is our error, and $A,B,C$ are our ``undetermined coefficients''"
    ]
   },
   {
@@ -1526,7 +1533,7 @@
  "metadata": {
   "celltoolbar": "Slideshow",
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   },
@@ -1540,7 +1547,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.8"
+   "version": "3.11.7"
   },
   "latex_envs": {
    "bibliofile": "biblio.bib",