From 21794905c6e1a1b55737bb496e21b020e722d4b5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Aur=C3=A9lien=20Geron?= <ageron@users.noreply.github.com>
Date: Fri, 18 May 2018 17:17:51 +0200
Subject: [PATCH] Improve formatting

---
 extra_autodiff.ipynb | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

diff --git a/extra_autodiff.ipynb b/extra_autodiff.ipynb
index cdcc42c..dbd3088 100644
--- a/extra_autodiff.ipynb
+++ b/extra_autodiff.ipynb
@@ -533,23 +533,23 @@
    "source": [
     "Dual numbers have their own arithmetic rules, which are generally quite natural. For example:\n",
     "\n",
-    "Addition:\n",
+    "**Addition**\n",
     "\n",
     "$(a_1 + b_1\\epsilon) + (a_2 + b_2\\epsilon) = (a_1 + a_2) + (b_1 + b_2)\\epsilon$\n",
     "\n",
-    "Subtraction:\n",
+    "**Subtraction**\n",
     "\n",
     "$(a_1 + b_1\\epsilon) - (a_2 + b_2\\epsilon) = (a_1 - a_2) + (b_1 - b_2)\\epsilon$\n",
     "\n",
-    "Multiplication:\n",
+    "**Multiplication**\n",
     "\n",
-    "$(a_1 + b_1\\epsilon) * (a_2 + b_2\\epsilon) = (a_1 a_2) + (a_1 b_2 + a_2 b_1)\\epsilon + b_1 b_2\\epsilon^2 = (a_1 a_2) + (a_1b_2 + a_2b_1)\\epsilon$\n",
+    "$(a_1 + b_1\\epsilon) \\times (a_2 + b_2\\epsilon) = (a_1 a_2) + (a_1 b_2 + a_2 b_1)\\epsilon + b_1 b_2\\epsilon^2 = (a_1 a_2) + (a_1b_2 + a_2b_1)\\epsilon$\n",
     "\n",
-    "Division:\n",
+    "**Division**\n",
     "\n",
     "$\\dfrac{a_1 + b_1\\epsilon}{a_2 + b_2\\epsilon} = \\dfrac{a_1 + b_1\\epsilon}{a_2 + b_2\\epsilon} \\cdot \\dfrac{a_2 - b_2\\epsilon}{a_2 - b_2\\epsilon} = \\dfrac{a_1 a_2 + (b_1 a_2 - a_1 b_2)\\epsilon - b_1 b_2\\epsilon^2}{{a_2}^2 + (a_2 b_2 - a_2 b_2)\\epsilon - {b_2}^2\\epsilon} = \\dfrac{a_1}{a_2} + \\dfrac{a_1 b_2 - b_1 a_2}{{a_2}^2}\\epsilon$\n",
     "\n",
-    "Power:\n",
+    "**Power**\n",
     "\n",
     "$(a + b\\epsilon)^n = a^n + (n a^{n-1}b)\\epsilon$\n",
     "\n",
@@ -560,7 +560,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Let's create a class to represent dual numbers, and implement a few operations (addition and multiplication). You try adding some more if you want."
+    "Let's create a class to represent dual numbers, and implement a few operations (addition and multiplication). You can try adding some more if you want."
    ]
   },
   {
@@ -618,7 +618,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "$(3 + 4ε)\\times(5 + 7ε) = 3 \\times 5 + 3 \\times 7ε + 4ε \\times 5 + 4ε \\times 7ε = 15 + 21ε + 20ε + 28ε^2 = 15 + 41ε + 28 \\times 0 = 15 + 41ε$"
+    "$(3 + 4ε)\\times(5 + 7ε)$ = $3 \\times 5 + 3 \\times 7ε + 4ε \\times 5 + 4ε \\times 7ε$ = $15 + 21ε + 20ε + 28ε^2$ = $15 + 41ε + 28 \\times 0$ = $15 + 41ε$"
    ]
   },
   {