In my previous PDE class we did nothing with method of chars. Now I am assigned one in a higher class, but all the examples I find online are not helpful for a particular problem I have. du/dt+a*du/dx=f(t,x) with u(0,x)=0 and f(t,x)=1 if -1<=x<=1, and f(t,x)= 0 otherwise Differences between this and typical examples I see in my PDE book and online: 1. I rarely see non-homogeneous ones. 2. Initial condition is NEVER equal to 0 in any example I've ever seen. 3. The solution I'm supposed to "show" is piecewise defined in 5 parts. I've seen a couple examples whose solution is defined into 2 parts, sometimes. But 5? Please be gentle.