Read: text, through chapter 3.

Do: "Problem 12c". Proceed as follows:

- Make a clear map of node numbers k=1 thru $N^2$. We will do this in class; stick to it.
- Make geometric arrays x(k), y(k), r(k), and theta(k); and write these to a file.
- As a test: Plot 2-D contours of r versus (x,y); and theta versus (x,y). They should look right, no surprises.

- Do everything with 32-bit words.
- For the matrix solution, use the subroutine Solve.f from the 105 library. Solve.f is for Real*4; Dsolve.f is for Real*8. Do not change these subroutines!
- Pay special attention to the plot of numerical error versus N. Use a log scale. Does it agree with theory? Why or why not?

- The Analytic Solution is derived here. You should verify that this solves the PDE and fits the BC's.

- For matrix solution:
- Use the Solve Routines. Solve.f is for Real*4; DSolve.f is for Real*8
- Banded Matrix Storage Modes. The Solve.f family uses Storage Mode 2.