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/laplace-transform/index.md | 21 +++++++--------------
 1 file changed, 7 insertions(+), 14 deletions(-)

(limited to 'source/know/concept/laplace-transform/index.md')

diff --git a/source/know/concept/laplace-transform/index.md b/source/know/concept/laplace-transform/index.md
index c7f352a..94c3742 100644
--- a/source/know/concept/laplace-transform/index.md
+++ b/source/know/concept/laplace-transform/index.md
@@ -35,6 +35,7 @@ using [partial fraction decomposition](/know/concept/partial-fraction-decomposit
 and then looking up the individual terms.
 
 
+
 ## Derivatives
 
 The derivative of a transformed function is the transform
@@ -55,11 +56,8 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-<div class="accordion">
-<input type="checkbox" id="proof-dv-s"/>
-<label for="proof-dv-s">Proof</label>
-<div class="hidden" markdown="1">
-<label for="proof-dv-s">Proof.</label>
+
+{% include proof/start.html id="proof-dv-s" -%}
 The exponential $$\exp(- s t)$$ is the only thing that depends on $$s$$ here:
 
 $$\begin{aligned}
@@ -69,9 +67,8 @@ $$\begin{aligned}
     &= \int_0^\infty (-t)^n f(t) \exp(- s t) \dd{t}
     = (-1)^n \hat{\mathcal{L}}\{t^n f(t)\}
 \end{aligned}$$
+{% include proof/end.html id="proof-dv-s" %}
 
-</div>
-</div>
 
 The Laplace transform of a derivative introduces the initial conditions into the result.
 Notice that $$f(0)$$ is the initial value in the original $$t$$-domain:
@@ -98,11 +95,8 @@ and $$f^{(0)}(t) = f(t)$$.
 As an example, $$\hat{\mathcal{L}}\{f'''(t)\}$$ becomes
 $$- f''(0) - s f'(0) - s^2 f(0) + s^3 \tilde{f}(s)$$.
 
-<div class="accordion">
-<input type="checkbox" id="proof-dv-t"/>
-<label for="proof-dv-t">Proof</label>
-<div class="hidden" markdown="1">
-<label for="proof-dv-t">Proof.</label>
+
+{% include proof/start.html id="proof-dv-t" -%}
 We integrate by parts and use the fact that $$\lim_{x \to \infty} \exp(-x) = 0$$:
 
 $$\begin{aligned}
@@ -116,8 +110,7 @@ $$\begin{aligned}
 
 And so on.
 By partially integrating $$n$$ times in total we arrive at the conclusion.
-</div>
-</div>
+{% include proof/end.html id="proof-dv-t" %}
 
 
 
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