### Homework assigned 10/20, due 10/23

### Adaptive Simpson's Rule

Choose a function that you know how to integrate. Put that
function in f.m and its antiderivative in f_int.m Choose an interval
of integration. Now use the adaptive Simpson's method *.m file to
integrate this function for a sequence of tolerances. Give me a table
that for each tolerance lists the tolerance, the number of nodes used,
the computed area, and then the error between the computed area and
the true area.

Choose a function for which an adaptive integration method will
be better than a standard uniform-mesh integration method. Explain
why an adaptive method will be better. Choose an interval of
integration. Again, use the adaptive Simpson's method *.m file to
integrate this function for a sequence of tolerances. Give me a table
that for each tolerance lists the tolerance, the number of nodes used,
and the computed area.

### Adaptive Trapezoidal Rule

Modify the adaptive Simpson's method *.m program to be an
adaptive trapezoidal method.

Repeat the first adaptive Simpson's method problem, to test that
your program is working. Use the same f.m and f_int.m. Compare the
two methods. What's the difference and why did you expect this
difference?

Repeat the second adaptive Simpson's method problem.

### Homework Amnesty

Hand in any late homework problems from the past six weeks.