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\textit{Oh, an empty article!} \title{Numerical Methods for conservation laws.}  \author{oogundipe }  \date{October 2015}  You can get started \maketitle  \paragraph{1. Modify the upwinding, Lax-Friedrichs, Lax-Wendroff subroutines given in class (or obtained/written  by \textbf{double clicking} this text block yourself) to solve}   \[  \left\{  \begin{array}{ll}  u_{t} + au_{x} = 0 \\  u(x, 0) = u_{0}(x)\\  u(0, t) = u(1, t)  \end{array}  \right.  \]  on $(x, t) \in [0, 1] \times [0, 5]$  \begin{itemize}  \item Your code should take spatial stepsize ∆x, a, $\lambda = a \Delta t$,  and begin editing. You can also click $u_0(x)$ as input.  \item The output is a video showing  the \textbf{Text} button below solution as time t goes from 0  to add new block elements. Or you can \textbf{drag and drop an image} right onto this text. Happy writing! 5.  \end{itemize}