The general form of quasi-linear PDEs is A(del u)/(del x)+B(del u)/(del t)=C(^(**)), where A, B, C are functions of u,x and t. The initial condition u(x;0) is specified at t=0,u(x,0)=f(x). We will convert the PDE to a sequence of ODEs, drastically simplifying its solution. This general technique is known as the method of characteristics and is useful for finding analytic and numerical solutions. To solve the PDE(**), we note that (A,B,C)*(u_(x),u_(t),-1)=0. (dot product) Recall from vector calculus that the normal to the surface f(x,y,z)=0 is grad f. To make the analogy here, t replaces y_(,)f(x,z)=u(x,t)-z and grad f=(u_(t),u_(x),-1). Thus, a plot of =-u(x,t) gives the surface f(x,t)=0. The vector (u_(x),u_(t),-1) is the normal to the solution.