From 6e70f28ccbd5afc1506f71f013278a9d157ef03a Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Thu, 27 Oct 2022 20:40:09 +0200
Subject: Optimize last images, add proof template, improve CSS
---
source/know/concept/fundamental-solution/index.md | 22 +++++++---------------
1 file changed, 7 insertions(+), 15 deletions(-)
(limited to 'source/know/concept/fundamental-solution')
diff --git a/source/know/concept/fundamental-solution/index.md b/source/know/concept/fundamental-solution/index.md
index 312cc2e..947aada 100644
--- a/source/know/concept/fundamental-solution/index.md
+++ b/source/know/concept/fundamental-solution/index.md
@@ -42,11 +42,8 @@ $$\begin{aligned}
}
\end{aligned}$$
-<div class="accordion">
-<input type="checkbox" id="proof-solution"/>
-<label for="proof-solution">Proof</label>
-<div class="hidden" markdown="1">
-<label for="proof-solution">Proof.</label>
+
+{% include proof/start.html id="proof-solution" -%}
$$\hat{L}$$ only acts on $$x$$, so $$x' \in ]a, b[$$ is simply a parameter,
meaning we are free to multiply the definition of $$G$$
by the constant $$f(x')$$ on both sides,
@@ -72,8 +69,8 @@ $$\begin{aligned}
By definition, $$\hat{L}$$'s response $$u(x)$$ to $$f(x)$$
satisfies $$\hat{L}\{ u(x) \} = f(x)$$, recognizable here.
-</div>
-</div>
+{% include proof/end.html id="proof-solution" %}
+
While the impulse response is typically used for initial value problems,
the fundamental solution $$G$$ is used for boundary value problems.
@@ -117,11 +114,8 @@ $$\begin{aligned}
}
\end{aligned}$$
-<div class="accordion">
-<input type="checkbox" id="proof-reciprocity"/>
-<label for="proof-reciprocity">Proof</label>
-<div class="hidden" markdown="1">
-<label for="proof-reciprocity">Proof.</label>
+
+{% include proof/start.html id="proof-reciprocity" -%}
Consider two parameters $$x_1'$$ and $$x_2'$$.
The self-adjointness of $$\hat{L}$$ means that:
@@ -135,9 +129,7 @@ $$\begin{aligned}
G^*(x_2', x_1')
&= G(x_1', x_2')
\end{aligned}$$
-
-</div>
-</div>
+{% include proof/end.html id="proof-reciprocity" %}
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