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') 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 @@ $$\begin{aligned} } \end{aligned}$$ -
- - - -
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 $$- f''(0) - s f'(0) - s^2 f(0) + s^3 \tilde{f}(s)$$. -
- - - -
+{% include proof/end.html id="proof-dv-t" %} -- cgit v1.2.3