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misc4

Maths Notation

$$ \frac{dx'}{dt}(\rho,t)\Big|_{t=0} = 0 \hspace{3cm} (3.4) $$ $$ \frac{dx'}{dt}(\rho,t_0) = 0 \hspace{3cm} (3.4) $$

$$ \frac{dy'}{dt}(\rho,t)\Big|_{t=0} = x(\rho,0) \hspace{3cm} (3.5) $$ $$ \frac{dy'}{dt}(\rho,t_0) = x(\rho,t_0) = x_0 \hspace{3cm} (3.5) $$

\begin{eqnarray} y'(\rho,t) & = & y'(\rho,t) - y'(\rho,t_0) \\ & = & \int_{t_0}^t \frac{dy'(\rho,s)}{ds} \; ds \\ & = & \frac{dy'(\rho,t_0)}{dt} \cdot \delta t + O(\delta t^2)\\ & = & x(\rho,t_0)\cdot \delta t + O(\delta t^2) \end{eqnarray}

misc4.txt · Last modified: 2018/08/16 16:38 by potthast