MATLAB.1

  Texts:
[B-D] Boyce & Diprima, Elementary Diff. Eq. & B.V. Problems, 9th Ed
[P-A]  Polking & Arnold,  ODEs using MATLAB, 2nd Ed                                                                    
A. Getting Started with MATLAB                                                 
                  
  Read Chapters 1 and 3 in Polking. Do this before trying to go on.
  
B. More on Functions

  Once a function y=g(x) is defined with a M-file you now know how to
  graph it on an interval [a,b] using the plot command.First you partition
  [a,b]. Next you evaluate g at these values . The plot command then
  plots these vertices connecting them by lines to give a piecewise
  linear approximation to the graph of g.

example:  Plot sin(x^2) on [-1,4]. First we make a M-file.

************************************************************

function y=g(x)
y=sin(x.^2);

************************************************************
 Go to the command window and type:

***********************************************************
x=-1:.1:4;
plot(x,g(x))
title('y=sin(x^2)')

***********************************************************

Note x=[-1,-.9,..,3.9,4] and g(x)=[g(-1),g(-.9),..,g(3.9),g(4)] .
 
 The graph is pretty crude because g oscillates more as  x increases.
 A second  way to graph is with the command fplot.
 
 example:  (continued)

Go to the command window and type:

***********************************************************
fplot('g(x)',[-1,4])
***********************************************************

One of the conveniences of fplot is , given g.m , it determines how 
fine the partition of [a,b] needs to be (what the vector x should
be) so that the piecewise linear approximation gives an accurate
picture. A second feature of fplot is that it does not require
g.m to be written with array smart notation as is required when 
using plot .
CAUTION!!  Don't name a function y(x) (that is, use the file y.m);
fplot will not plot it. Also fplot only recognizes "x" as the independent
variable. So type "fplot('g(x)',[-1,4])" ,not  "fplot('g(t)',[-1,4])"
even if you used  "t" as the independent variable in g.m.



ASSIGNMENT 1 :
A. a) Let A= 1  7      B= -3  2      C= 3  4  1 
             0 -3          3 -2        -2 -1  4
                                        0 -4  3 

         v=[3 5]'     w=[2 -9]'   x=[-4  3]    y=[0  6 -3].
 
Note  []' is the transpose of [].

In MATLAB, find from the following the combinations which are not defined and 
explain in each case why.

A*A  A*B  A*C  A.*A  A+B  A+C  A./C  A.\B

A*x  x*A  v*A  x.*A  A.*x  y*C  C*x  C*y

A*v  A*w  x+v  v+w  x*x  v.*w  w.*v  y.^2

y^2  A^2  x+y  v*y  v.*y  v*w  x*w  x.*w

 b) Show that A= 1 -2   and  B= -2 -3   commute.
                 0  3            0  1




B.Graph f(x) = cos(x.^4) on [0,2].
  a) Use the plot command with subintervals of length h =.2.
  b) Use fplot.
 
 FOR ALL OF YOUR MATLAB GRAPHING HOMEWORK FOR THIS COURSE TITLE YOUR GRAPHS .