From 18811c2d092cd6e9a60b279a41e54fbb70310581 Mon Sep 17 00:00:00 2001 From: Worker Agent Date: Thu, 4 Jun 2026 19:10:58 -0500 Subject: [PATCH] fix(appB): correct Laplace derivative formula --- appendices/appB_transform_tables.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/appendices/appB_transform_tables.tex b/appendices/appB_transform_tables.tex index 6bbcb3f..c4d14ef 100644 --- a/appendices/appB_transform_tables.tex +++ b/appendices/appB_transform_tables.tex @@ -63,7 +63,7 @@ The following algebraic and operational properties make the Laplace transform a Linearity & $\mathcal{L}\{a f(t) + b g(t)\} = a F(s) + b G(s)$ \\[6pt] First shift & $\mathcal{L}\{e^{at}f(t)\} = F(s-a)$ \\[6pt] Second shift & $\mathcal{L}\{u_{c}(t)\,f(t-c)\} = e^{-cs}F(s)$ \\[6pt] -Derivative & $\mathcal{L}\{f'(t)\} = s F(s) - s f(0)$ \\[6pt] +Derivative & $\mathcal{L}\{f'(t)\} = s F(s) - f(0)$ \\[6pt] Second derivative & $\mathcal{L}\{f''(t)\} = s^{2}F(s) - s f(0) - f'(0)$ \\[6pt] $n$th derivative & $\mathcal{L}\{f^{(n)}(t)\} = s^{n}F(s) - s^{n-1}f(0) - \cdots - f^{(n-1)}(0)$ \\[6pt] Integral & $\displaystyle \mathcal{L}\!\left\{\int_{0}^{t} f(\tau)\,\diff\tau\right\} = \frac{F(s)}{s}$ \\[8pt]