Math 30650, Spring 2009
Assignment 2, due February 6
ALERT: You have two weeks to do this assignment. Aim to complete as much
as possible in the first week. Make sure you know Eulerās method and understand
the standard notation (the notation in Boyce and DiPrima) for it by January 30.
Reread Section 4.4 and read Sections 8.1, 8.3, 8.5, 7.1-7.3 in Boyce and DiPrima
(in that order) and read Differential Equations with MATLAB R
ī, Chapters 5, 7 and
8.
Do:
p. 240 #4
Problem Set C #1,8,10,16,17 in Differential Equations with MATLAB R
ī. Also,
add the following part to #16:
#16 (e) Modify the program to implement the Runge-Kutta method and repeat
parts (a) and (b) using the Runge-Kutta Method. Also use the Runge-Kutta Method
with the same step sizes as in (a) and (b) on the interval 0 ā¤xā¤10. Compare the
plots for the two methods.
In #1, in MATLAB 7.7 you may have trouble interpreting the answer dsolve
gives in (a). Also, dsolve cannot solve the problem in (b). Here are other ways to
solve the the two equations (explain how you obtained the solutions):
ā¢Solve by handāthe equations are separable. (In (b), use the substitution u=
ey+ 1 to carry out the yintegral.)
ā¢Use MATLAB 7.5 on a linux computer in the engineering cluster. You can do
this with the command /opt/und/matlab/7.5/bin/matlab
ā¢Use Maple, which is available on all cluster computers, except maybe some of
the computers in the library. To solve, e.g., y0= 5y, y(0) = 7 with Maple, give
the command: dsolve(diff(y(t), t) = 5*y(t), y(0) = 7)
ā¢Use Mathematica. (Iām not a Mathematica user, so youāre on your own here.)
In #8(b), there are three minor typos - each xin a displayed equation should be
changed to tand in the integral, dt should be changed to ds.
In #16(a) and (b) you do not need to show the commands for the Euler Method
since that is given in the book. You do not need to display the values the method
computes. In #16(e) you must show your commands for the Runge-Kutta method.
You can do this, for example, by creating a function Mfile myrungekutta.m for the
method and then giving the command type myrungekutta.
On this assignment (including the Bonus Problems) you may work on the MAT-
LAB problems in a group of at most three students. If you work in a group, the group
