From 511d67cbae8ab37ee987298d61d30debf2637763 Mon Sep 17 00:00:00 2001 From: David Rotermund <54365609+davrot@users.noreply.github.com> Date: Sat, 6 Jan 2024 16:24:13 +0100 Subject: [PATCH] Update README.md Signed-off-by: David Rotermund <54365609+davrot@users.noreply.github.com> --- matlab/8/README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/matlab/8/README.md b/matlab/8/README.md index 6acddb1..df70e01 100644 --- a/matlab/8/README.md +++ b/matlab/8/README.md @@ -243,9 +243,9 @@ It can be seen that $$\vec{F}\left(\vec{x}\,^*(t+\frac{\tau}{2}),t+\frac{\tau}{2}\right) =$$ -$$= \vec{F}(\vec{x},t)+\frac{\partial \vec{F}}{\partial \vec{x}}\Big|_{(\vec{x},t)}\vec{F}(\vec{x},t)\frac{\tau}{2}+ \frac{\partial \vec{F}}{\partial t}\Big|_{(\vec{x},t)}\frac{\tau}{2} +{\cal O}(\tau^2)$$ +$$= \vec{F}(\vec{x},t)+ \left. \frac{\partial \vec{F}}{\partial \vec{x}}\right\vert_{(\vec{x},t)}\vec{F}(\vec{x},t)\frac{\tau}{2}+ \left. \frac{\partial \vec{F}}{\partial t}\right\vert_{(\vec{x},t)}\frac{\tau}{2} +{\cal O}(\tau^2)$$ -$$= \dot{\vec{x}}(t)+\left(\frac{\partial \vec{F}}{\partial \vec{x}}\Big|_{(\vec{x},t)}\dot{\vec{x}}(t)+ \frac{\partial \vec{F}}{\partial t}\Big|_{(\vec{x},t)}\right)\frac{\tau}{2}+ {\cal O}(\tau^2)$$ +$$= \dot{\vec{x}}(t)+\left(\left. \frac{\partial \vec{F}}{\partial \vec{x}}\right\vert_{(\vec{x},t)}\dot{\vec{x}}(t)+ \left. \frac{\partial \vec{F}}{\partial t}\right\vert_{(\vec{x},t)}\right)\frac{\tau}{2}+ {\cal O}(\tau^2)$$ $$= \dot{\vec{x}}(t)+ \ddot{\vec{x}}(t)\frac{\tau}{2}+ {\cal O}(\tau^2) \, .$$