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Diffstat (limited to 'source/know/concept/impulse-response/index.md')
| -rw-r--r-- | source/know/concept/impulse-response/index.md | 10 |
1 files changed, 3 insertions, 7 deletions
diff --git a/source/know/concept/impulse-response/index.md b/source/know/concept/impulse-response/index.md index 397ac2d..661ed3f 100644 --- a/source/know/concept/impulse-response/index.md +++ b/source/know/concept/impulse-response/index.md @@ -30,11 +30,8 @@ $$\begin{aligned} } \end{aligned}$$ -<div class="accordion"> -<input type="checkbox" id="proof-main"/> -<label for="proof-main">Proof</label> -<div class="hidden" markdown="1"> -<label for="proof-main">Proof.</label> + +{% include proof/start.html id="proof-theorem" -%} Starting from the definition of $$u_p(t)$$, we shift the argument by some constant $$\tau$$, and multiply both sides by the constant $$f(\tau)$$: @@ -60,9 +57,8 @@ $$\begin{aligned} \hat{L} \int_0^\infty f(\tau) \: u_p(t - \tau) \dd{\tau} &= (f * u_p)(t) = \hat{L}\{ u(t) \} = f(t) \end{aligned}$$ +{% include proof/end.html id="proof-theorem" %} -</div> -</div> This is useful for solving initial value problems, because any initial condition can be satisfied |