in the form of equation (12b), page 97.
Reading: Claerbout, sections 2.0-2.2 .
The exercises in light gray color are extra credit and are not required.
1. Claerbout, p. 90, exercise 1. Consider a tilted straight line tangent to a circle. Use this line to initialize the Muir square-root expansion. State equations and plot them (-2 <= X <= +2) for the next two Muir semicircle approximations. Just plot S1 and S2 on graph paper.
2. Claerbout, p. 102, exercise 1. Interpret the inflation-of-money equation when the interest rate is the imaginary number i/10. Describe how it behaves for increasing t.
3.
Claerbout, p. 102, exercise 2.
Write the 45-degree diffraction equation in (x,z)-space for fixed
in the form of equation (12b), page 97.
4.
By what percentage does the Muir square root expansion overestimate
for the
5, 15, and 45 degree approximations at each of these
angles (all three angles for each approximation)?
5. Run the explicitly and implicitly finite-differenced heat-flow equations using ``exhf.java'' and ``imhf.java''. What kind of side boundaries do they use?
6. Convert ``exhf.java'' to use the leapfrog method in time. What happens? Run it and turn in the output. Copy and paste the output text from the Java Console, DOS window, or CommandTool into your text editor to print it.
7. Suppose we had the transformation x' = x, z' = z, and t' = t - z/v, a downgoing coordinate system. Derive retarded paraxial wave equations for both the upgoing and downgoing paraxial equations in the 5 and 15 degree cases.