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v14	v15
16	16	[[latex($\int^{x_2}_{x_1} U(x,t_2) \ \mathrm{d}x = \int_{x_1}^{x_2} U(x,t_1) \ \mathrm{d}x + \int_{t_1}^{t_2}F(U(x_1,t)) \ \mathrm{d}t - \int_{t_1}^{t_2} F(U(x_2,t)) \ \mathrm{d}t \hspace{1 in} (1)$)]]
17	17
18		In this form, it might be easier to see that the change in ~~conserved quantity is equal to the flux coming into the volume minus the~~ flux going out of the volume.
	18	In this form, it might be easier to see that the change in a conserved quantity is equal to its flux coming into the volume minus its flux going out of the volume.
19	19	== Solving the Riemann Problem ==
20	20	The Riemann problem is essentially the Euler equations with discrete initial conditions. Initial data has a left state and a right state, separated by a discontinuity.