1. The problem statement, all variables and given/known data How were the integral lines dt/a = dx/b derived from the PDE aUt + bUx = 0 where Ut is the partial derivative with respect to time and Ux with respect to x and a, b are constants. 2. Relevant equations I honestly have no idea. I may be unprepared for this course as Strauss's book feels like it's skipping through a lot of steps. If anyone could by chance explain or guide me to an explanation of how the Method of Characteristics (which I think is related here?) works that would be amazing. I just don't see how the system of ODEs comes from a PDE in the manner, for example, described here: http://www.stanford.edu/class/math220a/handouts/firstorder.pdf In particular where it says "...Curve C will satisfy the following system..." Again, any help would be much appreciated. I'm more looking for a reason why all this should work.