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 $$\vec{F}\left(\vec{x}\,^*(t+\frac{\tau}{2}),t+\frac{\tau}{2}\right) =$$ -$$= \vec{F}(\vec{x},t)+\frac{\partial \vec{F}}{\partial \vec{x}}\Big|_{(\vec{x},t)}\vec{F}(\vec{x},t)\frac{\tau}{2}+ \frac{\partial \vec{F}}{\partial t}\Big|_{(\vec{x},t)}\frac{\tau}{2} +{\cal O}(\tau^2)$$ +$$= \vec{F}(\vec{x},t)+ \left. \frac{\partial \vec{F}}{\partial \vec{x}}\right\vert_{(\vec{x},t)}\vec{F}(\vec{x},t)\frac{\tau}{2}+ \left. \frac{\partial \vec{F}}{\partial t}\right\vert_{(\vec{x},t)}\frac{\tau}{2} +{\cal O}(\tau^2)$$ -$$= \dot{\vec{x}}(t)+\left(\frac{\partial \vec{F}}{\partial \vec{x}}\Big|_{(\vec{x},t)}\dot{\vec{x}}(t)+ \frac{\partial \vec{F}}{\partial t}\Big|_{(\vec{x},t)}\right)\frac{\tau}{2}+ {\cal O}(\tau^2)$$ +$$= \dot{\vec{x}}(t)+\left(\left. \frac{\partial \vec{F}}{\partial \vec{x}}\right\vert_{(\vec{x},t)}\dot{\vec{x}}(t)+ \left. \frac{\partial \vec{F}}{\partial t}\right\vert_{(\vec{x},t)}\right)\frac{\tau}{2}+ {\cal O}(\tau^2)$$ $$= \dot{\vec{x}}(t)+ \ddot{\vec{x}}(t)\frac{\tau}{2}+ {\cal O}(\tau^2) \, .$$