test2

63a317d8 · Tom van Woudenberg · 6bd1a1ee · 63a317d8
Commit 63a317d8 authored 6 months ago by Tom van Woudenberg
--- a/book/numerical_methods/taylor-series-exercise.ipynb
+++ b/book/numerical_methods/taylor-series-exercise.ipynb
@@ -13,7 +13,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 20,
   "metadata": {
    "tags": [
     "thebe-remove-input-init"
@@ -28,7 +28,7 @@
    "\n",
    "import operator\n",
    "import ipywidgets as widgets\n",
-    "#from IPython.display import display, Latex, display_jpeg, Math, Markdown\n",
+    "from IPython.display import Latex, Math\n",
    "sp.init_printing()\n",
    "#sp.init_printing(use_latex=True)\n",
    "\n",
@@ -54,8 +54,8 @@
    "    def _show_correct_answer(button):\n",
    "        with correct_output:\n",
    "            correct_output.clear_output()  # Clear previous outputs\n",
-    "            print(f\"The correct answer is: {sp.latex(expected)}\")\n",
-    "            display(expected)\n",
+    "            print(f\"The correct answer is in python notation: {str(expected)}\")\n",
+    "            print(f\"Or in mathematical notation: {expected}\")\n",
    "            \n",
    "    \n",
    "    button.on_click(_inner_check)\n",
@@ -139,18 +139,75 @@
   },
   "outputs": [],
   "source": [
-    "eq1_answer = 1"
+    "eq1_answer = "
   ]
  },
  {
   "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 21,
   "metadata": {
    "tags": [
     "thebe-remove-input-init"
    ]
   },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "9cd040484fe340f0a91d3884877d989d",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Button(description='Check answer', style=ButtonStyle())"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "301cadbc376842ee8b5b194f88b73b0f",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Output()"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "e838a70e34e64af8aa9974820b2b7437",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Button(description='Show correct answer', style=ButtonStyle())"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "ca9f2dc0fa7142e5978ce258319a943f",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Output()"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
   "source": [
    "check_answer(\"eq1_answer\",eq1_correct, check_equation)\n"
   ]

 %% Cell type:markdown id: tags:

 # Exercises on Taylor expansion

 This page shows some exercises on calculating Taylor expansions. If you reload this page, you'll get new values.

 Click `rocket` -->`Live Code` to start practising.

 %% Cell type:code id: tags:thebe-remove-input-init

 ``` python
 import sympy as sp
 import numpy as np
 from sympy import pi, latex
 #from sympy.printing.mathml import mathml

 import operator
 import ipywidgets as widgets
-#from IPython.display import display, Latex, display_jpeg, Math, Markdown
+from IPython.display import Latex, Math
 sp.init_printing()
 #sp.init_printing(use_latex=True)


 check_equation = lambda eq1, eq2: sp.simplify(eq1 - eq2) == 0

 def check_answer(variable_name, expected, comparison=operator.eq):
    output = widgets.Output()
    correct_output = widgets.Output()
    button = widgets.Button(description="Check answer")
    show_correct_button = widgets.Button(description="Show correct answer")

    def _inner_check(button):
        with output:
            if comparison(globals()[variable_name], expected):
                output.outputs = [{'name': 'stdout', 'text': 'Correct!',
                                   'output_type': 'stream'}]
                correct_output.clear_output()  # Clear the correct answer display if they got it right
            else:
                output.outputs = [{'name': 'stdout', 'text': 'Incorrect!',
                                   'output_type': 'stream'}]

    def _show_correct_answer(button):
        with correct_output:
            correct_output.clear_output()  # Clear previous outputs
-            print(f"The correct answer is: {sp.latex(expected)}")
-            display(expected)
+            print(f"The correct answer is in python notation: {str(expected)}")
+            print(f"Or in mathematical notation: {expected}")


    button.on_click(_inner_check)
    show_correct_button.on_click(_show_correct_answer)

    display(button, output, show_correct_button, correct_output)



 ```

 %% Cell type:markdown id: tags:


 ## Exercise 1

 Calculate the taylor series expansion of:

 %% Cell type:code id: tags:thebe-remove-input-init

 ``` python
 x, y = sp.symbols('x, y')
 a_1 = sp.Integer(np.random.randint(2,6))
 b_1 = sp.Integer(np.random.randint(-10,10))
 c_1 = sp.Integer(np.random.randint(-5,5))
 eq1_original = a_1 * x**2 + b_1*x
 eq1_correct = sp.series(eq1_original,x,c_1)
 eq1_answer = 0
 display(eq1_original)
 #display(eq1_correct)
 ```

 %% Cell type:markdown id: tags:

 around:

 %% Cell type:code id: tags:thebe-remove-input-init

 ``` python
 display(sp.Eq(x,c_1))
 ```

 %% Cell type:markdown id: tags:

 Discard any $O(x^3)$ terms.

 Fill in your answer and run the cell before clicking 'Check answer'.

 %% Cell type:code id: tags:auto-execute-page,disable-download-page

 ``` python
-eq1_answer = 1
+eq1_answer =
 ```

 %% Cell type:code id: tags:thebe-remove-input-init

 ``` python
 check_answer("eq1_answer",eq1_correct, check_equation)
 ```

+%% Output
+
+
+
+
+
 %% Cell type:markdown id: tags:

 ## Exercise 2

 Calculate the taylor series expension of:

 %% Cell type:code id: tags:thebe-remove-input-init

 ``` python
 a_2 = sp.Integer(np.random.randint(1,7))
 c_2 = sp.Integer(np.random.randint(-5,5))
 eq2_original = a_2*sp.tan(x)
 display(eq2_original)
 eq2_correct = sp.series(eq2_original,x,c_2*sp.pi,3).removeO()
 #display(eq2_correct)
 eq2_answer = 0
 ```

 %% Cell type:markdown id: tags:

 around:

 %% Cell type:code id: tags:thebe-remove-input-init

 ``` python
 display(sp.Eq(x,c_2*sp.pi))
 ```

 %% Cell type:markdown id: tags:

 discard any $O(x^3)$ terms.

 Fill in your answer and run the cell before clicking 'Check answer'. Furthermore, use `pi` for $\pi$:

 %% Cell type:code id: tags:

 ``` python
 eq2_answer =
 ```

 %% Cell type:code id: tags:thebe-remove-input-init

 ``` python
 check_answer("eq2_answer",eq2_correct, check_equation)
 ```

 %% Cell type:markdown id: tags:

 ## Exercise 3

 Calculate the taylor series expension of:

 %% Cell type:code id: tags:thebe-remove-input-init

 ``` python
 a_3 = sp.Integer(np.random.randint(1,10))
 c_3 = sp.Integer(np.random.randint(-1,1))
 eq3_original = a_3 / (1 - x)
 display(eq3_original)
 eq3_correct = sp.series(eq3_original,x,c_3,3).removeO()
 #display(eq3_correct)
 eq3_answer = 0
 ```

 %% Cell type:markdown id: tags:

 around:

 %% Cell type:code id: tags:thebe-remove-input-init

 ``` python
 display(sp.Eq(x,c_3))
 ```

 %% Cell type:markdown id: tags:

 discard any $O(x^3)$ terms.

 Fill in your answer and run the cell before clicking 'Check answer':

 %% Cell type:code id: tags:

 ``` python
 eq3_answer =
 ```

 %% Cell type:code id: tags:thebe-remove-input-init

 ``` python
 check_answer("eq3_answer",eq3_correct, check_equation)
 ```