Math 5385
Supplementary Matlab exercises #1, #2, and #3
Exercise 1
In this exercise, we define C to be the plane curve
y2 = x2 - x4,
- Is the origin a point of C?
- Use the Matlab script aPlot to plot C
in the region -1.2 < x < 1.2,
-1 < y < 1, in each of the following ways:
- with a 100 by 100 grid;
- with a 51 by 51 grid;
- with a 500 by 500 grid.
- Which of the plots are more accurate than the others? What features
could be contributing to this situation?
Exercise 2
- Use the Matlab script aPlot to plot the plane curve
y2 = x4 + y4,
in the region -1 < x < 1,
-1.2 < y < 1.2, in each of the following ways:
- with a 51 by 51 grid;
- with a 501 by 501 grid;
- with a 1000 by 1000 grid.
- Answer the same questions as in Part c of Exercise 1.
- (Challenge question) Can you identify what feature makes
this curve "worse" than the curve of Exercise 1?
Exercise 3
Consider the following family of plane cubic curves:
y2 = x3 - 3x + c
Plot 6 curves in this family, corresponding to the following parameter
values:
- c = 2
- c = -2
- A value of c slightly above c = 2
and a
value of c slightly below c = 2.
- A value of c slightly above c = -2
and a
value of c slightly below c = -2.
Print a picture that includes all 6 curves, with distinct colors or patterns,
and suitable labels.
Alternatively if this is too cluttered, print 2 pictures, each
including 3 curves.
Notes:
- If you don't have access to
a color printer, you may print to a file or files (postscript, jpeg, or pdf),
and then e-mail that file {or those files} to me.
- I usually don't grade on neatness or appearance, but these
exercises are a definite exception to that rule.
Indeed, the
point here is to make a drawing (or drawings) which will show the viewer what's
going on.
If you can draw all 6 curves on 1 sketch, with suitably
contrasting colors and separation, that would be wonderful.
Otherwise
maybe you can separate them, perhaps into 2 drawings, each with 3 curves.
- If using equally spaced parameter values, then the Matlab
script family could be useful.
- Otherwise, if adding curves one by one to your sketch, then the Mablab
command hold on is very useful.
- It's also possible to combine the two previous suggestions,
for instance if you're using 2 groups of 3 closely spaced parameter values.
- There is a feature of the curve corresponding to c = -2
that Matlab won't show you,
but I may not divulge particulars about
this before the due date of the assignment.
Comments and questions to:
roberts@math.umn.edu
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