diff --git a/lectures/approximation/approximation_auxiliary.py b/lectures/approximation/approximation_auxiliary.py
index 530fac0..619ce8c 100644
--- a/lectures/approximation/approximation_auxiliary.py
+++ b/lectures/approximation/approximation_auxiliary.py
@@ -2,13 +2,7 @@
 
 
 def get_uniform_nodes(n, a=-1, b=1):
-
-    nodes = np.tile(np.nan, n)
-
-    for i in range(1, n + 1):
-        nodes[i - 1] = a + (i - 1) / (n - 1) * (b - a)
-
-    return nodes
+    return np.linspace(a, b, num=n)
 
 
 def get_chebyshev_nodes(n, a=-1, b=1):
diff --git a/lectures/approximation/approximation_plots.py b/lectures/approximation/approximation_plots.py
index e813b43..b61ed9c 100755
--- a/lectures/approximation/approximation_plots.py
+++ b/lectures/approximation/approximation_plots.py
@@ -8,6 +8,7 @@
 from approximation_problems import problem_reciprocal_exponential
 from approximation_problems import problem_runge
 from numpy.polynomial import Chebyshev as T
+from numpy.polynomial import Polynomial as P
 
 
 def plot_problem_runge():
@@ -28,8 +29,8 @@ def plot_runge_multiple():
 
     for degree in [5, 9]:
         xnodes = np.linspace(a, b, degree)
-        c = np.polyfit(xnodes, problem_runge(xnodes), degree)
-        yfit = np.polyval(c, xvals)
+        poly = P.fit(xnodes, problem_runge(xnodes), degree)
+        yfit = poly(xvals)
         ax.plot(xvals, yfit, label=" 9th-order")
 
     ax.legend()
@@ -56,11 +57,11 @@ def plot_reciprocal_exponential(a=-5, b=5):
     ax.plot(yvals, problem_reciprocal_exponential(yvals))
 
 
-def plot_approximation_nodes(num_nodes, strategy="uniform"):
+def plot_approximation_nodes(num_nodes, nodes="uniform"):
 
-    if strategy == "uniform":
+    if nodes == "uniform":
         get_nodes = get_uniform_nodes
-    elif strategy == "chebychev":
+    elif nodes == "chebychev":
         get_nodes = get_chebyshev_nodes
 
     fig, ax = plt.subplots()
diff --git a/lectures/approximation/approximation_solutions_exercises.py b/lectures/approximation/approximation_solutions_exercises.py
index 338b57d..8eaf329 100644
--- a/lectures/approximation/approximation_solutions_exercises.py
+++ b/lectures/approximation/approximation_solutions_exercises.py
@@ -10,7 +10,7 @@
 
 def test_exercise_1():
 
-    index = product([10, 20, 30, 40, 50], np.linspace(-5, 5, 1000))
+    index = product([10, 20, 30, 40, 50], np.linspace(-1, 1, 1000))
 
     index = pd.MultiIndex.from_tuples(index, names=("Degree", "Point"))
     df = pd.DataFrame(columns=["Value", "Approximation"], index=index)
@@ -19,7 +19,7 @@ def test_exercise_1():
 
     for degree in [10, 20, 30, 40, 50]:
 
-        xnodes = get_uniform_nodes(degree, -5, 5)
+        xnodes = get_uniform_nodes(degree, -1, 1)
         poly = P.fit(xnodes, problem_runge(xnodes), degree)
 
         xvalues = df.index.get_level_values("Point").unique()
diff --git a/lectures/approximation/notebook.ipynb b/lectures/approximation/notebook.ipynb
index 5b9d835..73ce9b8 100644
--- a/lectures/approximation/notebook.ipynb
+++ b/lectures/approximation/notebook.ipynb
@@ -59,7 +59,7 @@
     "Regardless of how the $n$ basis functions and nodes are chosen, computing the basis coefficients reduces to solving a linear equation.\n",
     "\n",
     "\\begin{align*}\n",
-    "\\sum_{j=1}^n = c_j \\phi_j(x) = f(x), \\qquad i = 1, ..., n\n",
+    "\\sum_{j=1}^n c_j \\phi_j(x) = f(x), \\qquad i = 1, ..., n\n",
     "\\end{align*}\n",
     "\n",
     "Interpolation schemes differ only in how the basis functions $\\phi_j$ and interpolation nodes $x_j$ are chosen.\n",
@@ -69,7 +69,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -143,7 +143,32 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\u001b[0;31mSignature:\u001b[0m \u001b[0mget_uniform_nodes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+       "\u001b[0;31mDocstring:\u001b[0m <no docstring>\n",
+       "\u001b[0;31mSource:\u001b[0m   \n",
+       "\u001b[0;32mdef\u001b[0m \u001b[0mget_uniform_nodes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
+       "\u001b[0;34m\u001b[0m    \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnum\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+       "\u001b[0;31mFile:\u001b[0m      ~/external-storage/ownCloud/office/OpenSourceEconomics/teaching/scientific-computing/course/lectures/approximation/approximation_auxiliary.py\n",
+       "\u001b[0;31mType:\u001b[0m      function\n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "??get_uniform_nodes"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
    "metadata": {},
    "outputs": [
     {
@@ -160,7 +185,7 @@
     }
    ],
    "source": [
-    "plot_approximation_nodes([5, 10, 15, 20], strategy=\"uniform\")"
+    "plot_approximation_nodes([5, 10, 15, 20], nodes=\"uniform\")"
    ]
   },
   {
@@ -172,7 +197,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -252,37 +277,6 @@
     "plot_basis_functions(\"monomial\")"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\u001b[0;31mSignature:\u001b[0m \u001b[0mget_uniform_nodes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-       "\u001b[0;31mDocstring:\u001b[0m <no docstring>\n",
-       "\u001b[0;31mSource:\u001b[0m   \n",
-       "\u001b[0;32mdef\u001b[0m \u001b[0mget_uniform_nodes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
-       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
-       "\u001b[0;34m\u001b[0m    \u001b[0mnodes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnan\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
-       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
-       "\u001b[0;34m\u001b[0m    \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
-       "\u001b[0;34m\u001b[0m        \u001b[0mnodes\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mb\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
-       "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
-       "\u001b[0;34m\u001b[0m    \u001b[0;32mreturn\u001b[0m \u001b[0mnodes\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-       "\u001b[0;31mFile:\u001b[0m      ~/external-storage/ownCloud/office/OpenSourceEconomics/teaching/scientific-computing/course/lectures/approximation/approximation_auxiliary.py\n",
-       "\u001b[0;31mType:\u001b[0m      function\n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "??get_uniform_nodes"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -296,7 +290,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -325,7 +319,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -342,7 +336,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
@@ -369,7 +363,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -393,9 +387,16 @@
     "</div>"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Since we have a good understanding what is causing the warning, we can simply turn it of going forward. A documentation that shows how to deal with more fine-grained filters is available [here](https://pymotw.com/3/warnings/)."
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -411,16 +412,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "<matplotlib.legend.Legend at 0x7f20237c4510>"
+       "<matplotlib.legend.Legend at 0x7fd0e8103890>"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -453,7 +454,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
@@ -478,7 +479,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
@@ -487,7 +488,7 @@
        "-0.3581719202049975"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -511,7 +512,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 34,
    "metadata": {},
    "outputs": [
     {
@@ -549,7 +550,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
@@ -587,7 +588,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [
     {
@@ -604,7 +605,7 @@
     }
    ],
    "source": [
-    "plot_approximation_nodes([5, 10, 15, 20], strategy=\"chebychev\")"
+    "plot_approximation_nodes([5, 10, 15, 20], nodes=\"chebychev\")"
    ]
   },
   {
@@ -623,7 +624,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
@@ -639,9 +640,7 @@
        "\u001b[0;34m\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;31mDocstring:\u001b[0m <no docstring>\n",
        "\u001b[0;31mSource:\u001b[0m   \n",
-       "\u001b[0;32mdef\u001b[0m \u001b[0mget_interpolator_monomial_flexible_nodes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\u001b[0m\n",
-       "\u001b[0;34m\u001b[0m    \u001b[0mfunc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdegree\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnodes\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"uniform\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\n",
-       "\u001b[0;34m\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
+       "\u001b[0;32mdef\u001b[0m \u001b[0mget_interpolator_monomial_flexible_nodes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdegree\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnodes\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"uniform\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mif\u001b[0m \u001b[0mnodes\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m\"uniform\"\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0mget_nodes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_uniform_nodes\u001b[0m\u001b[0;34m\u001b[0m\n",
@@ -666,7 +665,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [
     {
@@ -676,7 +675,7 @@
        "        0.1289,  0.0418, -0.0053])"
       ]
      },
-     "execution_count": 16,
+     "execution_count": 17,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -695,7 +694,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [
     {
@@ -738,7 +737,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 19,
    "metadata": {},
    "outputs": [
     {
@@ -827,7 +826,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [
     {
@@ -883,7 +882,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 21,
    "metadata": {},
    "outputs": [
     {