deletions | additions       diff --git a/First_step_in_Velocity_Verlet__.tex b/First_step_in_Velocity_Verlet__.tex  index ca33598..615cc98 100644  --- a/First_step_in_Velocity_Verlet__.tex  +++ b/First_step_in_Velocity_Verlet__.tex 
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$$\vec{v}(\Delta t) = \vec{v}(0) + \frac{1}{2}\vec{a}(0)\Delta t + \frac{1}{\Delta t} (\vec{x}(2 \Delta t) - \vec{x}(\Delta t) - \vec{v}(\Delta t) \Delta t)$$  $$2 \vec{v}(\Delta t) = \vec{v}(0) + \frac{1}{2}\vec{a}(0)\Delta t + \frac{1}{\Delta t} \vec{x}(2 (\vec{x}(2  \Delta t) -\frac{1}{\Delta t}  \vec{x}(\Delta t)$$ t))$$