Math 293, Homework 2, due Wed. 9/11/96

note:  MATLAB COURSE ACCOUNT AND PASSWORD
        Name:   Math293    (No spaces) 
        Pswd:   NoNumbrs   (Case sensitive)

O. 
If you have not learned any MATLAB in the past  and cannot get hold of any good 
MATLAB documentation, you get a free one week extension on the first computer homework
(HW 1, problem 4)

I.
The Math 293 list serve is now working.  We will start sending out messages  Wedensday 
9/4/96 including help with the homework. Send the following command via email to 
listproc@cornell.edu:

                      subscribe math293-L   yourfirstname lastname

II.
Please read over the General Course Information sheet carefully.

III
Make sure you can do problems 1.2.1-1.2.17 (solving special 1st and 2nd order equations 
by integration).  Once you see what these are about, the hard part is doing the 
integrals. For this purpose you can use a table of integrals, MAPLE, or MATHEMATICA.  
As a challenge and math review, you should see how many of the integrals you can do 
without looking anything up.

IV.
Try a few of problems 1.2.18-1.2.34 and make sure you can do problems of that type 
(word problems involving position and velocity for constant acceleration).

VI.
Computers have two uses in this class: 1) as a calculation tool for solving problems 
related to the material, and 2) as a pedagogical aid.  Your learning of MATLABs ODE23 
is the former use.  The latter use includes the program DFIELD.M and the functions 
it uses DFSOLVE.M and DFSOLVE.MEX written by John C. Polking of Rice University.  
These programs also {\it happen} to be written in MATLAB but are more sophisticated 
than anything you would be expected to be able to do. 

These programs are (or will be shortly) in a Math 293 folder on the Upson computers.  
They will also be emailed to you on Wedensday 9/4/96.

To use the program just open DFIELD from inside MATLAB. Read the first two paragraphs 
of comments and note the buttons and menus available for use.  To print a plot after 
you have made it just type   {\tt print} on the MATLAB command line.

Use this program to set up and do some problems of the type 1.3.1-1.3.10 (Use drawn 
slope fields to approximately graph 1st order ODE solutions).  Try drawing some graphs
by hand to compare to the curves drawn by the computer.

V.
Try a few of 1.3.21-1.3.30 and see if you get the idea of the conditions for existence 
and uniqueness. You might also try these with DFIELD to get a feel of the issues involved.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Problems to hand in
^^^^^^^^^^^^^^^^^^^

1.
Write:   I have read the general course information pages and have the following 
question(s) about course policy: (fill in any questions you have). 


2. 1.1.29 (Finding an ODE from a geometric description of the curve.)

3.
Here we start with a word problem and ask you to solve it 3 different ways.

a)
Turn this sentence into a differential equation:  `The velocity of a particle is 
proportional to sin(t).'
 
b)
Assume the proportionality constant is 2 and that the initial position is 3 
(in some consistent set of units). Re-write the equation and define the 'initial 
value problem'.

c)
Find x(t) using the method of problems 1.2.1-10 (integration). Also find x at t=\pi.

d)
Use DFIELD to get a graphical solution to (b) and compare your result.

e)
Use a modification of your solution to homework 1, problem 4 to get a solution using 
ODE23 (numerical integration that you control --- less canned than DFIELD).  Compare 
to the results of (c) and (d) }

4.
1.2.23  (Constant acceleration involving guns and bombs. The important part is going 
from words to equations.)

5.
1.3.31  OR (extra credit) 1.3.36. (Existence  and uniqueness stuff).





















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