From 16555851b6514a736c5c9d8e73de7da7fc9b6288 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Thu, 20 Oct 2022 18:25:31 +0200
Subject: Migrate from 'jekyll-katex' to 'kramdown-math-sskatex'

---
 source/know/concept/dirac-delta-function/index.md | 18 ++++++++++--------
 1 file changed, 10 insertions(+), 8 deletions(-)

(limited to 'source/know/concept/dirac-delta-function')

diff --git a/source/know/concept/dirac-delta-function/index.md b/source/know/concept/dirac-delta-function/index.md
index 88a08cb..518eba1 100644
--- a/source/know/concept/dirac-delta-function/index.md
+++ b/source/know/concept/dirac-delta-function/index.md
@@ -8,10 +8,10 @@ categories:
 layout: "concept"
 ---
 
-The **Dirac delta function** $\delta(x)$, often just the **delta function**,
+The **Dirac delta function** $$\delta(x)$$, often just the **delta function**,
 is a function (or, more accurately, a [Schwartz distribution](/know/concept/schwartz-distribution/))
 that is commonly used in physics.
-It is an infinitely narrow discontinuous "spike" at $x = 0$ whose area is
+It is an infinitely narrow discontinuous "spike" at $$x = 0$$ whose area is
 defined to be 1:
 
 $$\begin{aligned}
@@ -35,7 +35,7 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-$\delta(x)$ is thus quite an effective weapon against integrals. This may not seem very
+$$\delta(x)$$ is thus quite an effective weapon against integrals. This may not seem very
 useful due to its "unnatural" definition, but in fact it appears as the
 limit of several reasonable functions:
 
@@ -57,7 +57,7 @@ $$\begin{aligned}
     \:\:\propto\:\: \hat{\mathcal{F}}\{1\}
 \end{aligned}$$
 
-When the argument of $\delta(x)$ is scaled, the delta function is itself scaled:
+When the argument of $$\delta(x)$$ is scaled, the delta function is itself scaled:
 
 $$\begin{aligned}
     \boxed{
@@ -70,17 +70,18 @@ $$\begin{aligned}
 <label for="proof-scale">Proof</label>
 <div class="hidden" markdown="1">
 <label for="proof-scale">Proof.</label>
-Because it is symmetric, $\delta(s x) = \delta(|s| x)$.
-Then by substituting $\sigma = |s| x$:
+Because it is symmetric, $$\delta(s x) = \delta(|s| x)$$.
+Then by substituting $$\sigma = |s| x$$:
 
 $$\begin{aligned}
     \int \delta(|s| x) \dd{x}
     &= \frac{1}{|s|} \int \delta(\sigma) \dd{\sigma} = \frac{1}{|s|}
 \end{aligned}$$
+
 </div>
 </div>
 
-An even more impressive property is the behaviour of the derivative of $\delta(x)$:
+An even more impressive property is the behaviour of the derivative of $$\delta(x)$$:
 
 $$\begin{aligned}
     \boxed{
@@ -94,13 +95,14 @@ $$\begin{aligned}
 <div class="hidden" markdown="1">
 <label for="proof-dv1">Proof.</label>
 Note which variable is used for the
-differentiation, and that $\delta'(x - \xi) = - \delta'(\xi - x)$:
+differentiation, and that $$\delta'(x - \xi) = - \delta'(\xi - x)$$:
 
 $$\begin{aligned}
     \int f(\xi) \: \dv{\delta(x - \xi)}{x} \dd{\xi}
     &= \dv{}{x}\int f(\xi) \: \delta(x - \xi) \dd{x}
     = f'(x)
 \end{aligned}$$
+
 </div>
 </div>
 
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