11 04/02 F

1. 5.25. Also: (c) Assume that
   
   $$f(x) = e^{-\vert x-2\vert}$$
   
   
   In a single very neat plot, draw $u(x,1)$, $u(x,2)$, and $u(x,3)$ versus $x$.

2. 5.26b. Ignore the hint. Simplify your answer as much as possible. Draw the characteristic in the $x,y$-plane.

3. 5.27(a). Include a sketch of the characteristic lines. Is the solution you get valid everywhere?

4. 5.27(b). Do not try to use an initial condition written in terms of two different, related, variables. Get rid of either $x$ or $y$ in the condition. Then call the argument of your undetermined function $\gamma$ and rewrite its expression in terms of $\gamma$. Include a sketch of the characteristic lines.

5. 5.29