Math 4501: Numerical Applied Mathematics
		  Reading and Homework Assignment 11
			  Prof. Wickerhauser


You are encouraged to collaborate on homework, and to work additional
exercises from the indicated problem sections, although the homework
grade will be based only on the exercises listed below.  Please upload
your solutions to Canvas/Assignments using GradeScope.  LATE HOMEWORK
WILL NOT BE ACCEPTED.

Check your solutions to problems marked with an asterisk(*) against the
values in the textbook's Answers section, pp.646--672.

Read Chapter 9, Sections 9.1 through 9.3 of the text.

Do Exercise 4 of Section 9.1, p.463.
Do Exercise 6 of Section 9.1, p.463.

Do Exercise 7 of Section 9.2, p.473.

Do Exercise 6 of Section 9.3, p.480.


Problem H11.1.  Write a computer program to solve the following initial value
problem on the interval [0,1]:

	y'(t) = 2*t*y(t), for 0<t<1;     y(0)=1

using Euler's method.  Have the program prompt the user for the number of
steps N, then use h=1/N as the step size.  Make a table of the values y(1)
for N=10, N=1000, and N=100,000.


Problem H11.2.  Write a computer program to solve the initial value problem
of Extra Problem H11.1 using Heun's method.  As before, have the program
prompt for the number of steps N and use h=1/N as the step size.  Make a
table of the values y(1) for N=10, N=1000, and N=100,000.  Compare the
results with those of Problem H11.1 and with the exact value:

        e=2.71828 18284 59045 23536 02874....