Matlab-2.doc
|MAT 274 |Elementary Differential Equations |Fall 1995 |
MATLAB 1.2: Creating matrices and first plots
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Objectives:
Getting started on learning alternatives how to efficiently create large matrices.
Rationale:
Three-by-three matrices are fine examples when studying most theoretical aspects in linear algebra.
In realistic applications thirty-by-thirty (or even 3000 by 3000) matrices are not at all uncommon.
Nobody would want to enter these by hand, component by component.
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1. The graph of a (scalar) function (of one variable):
Recall making a table of function values (by hand or EXCEL), plotting it point by point, connecting the dots.
In MATLAB it is done in a way very similar to EXCEL: First create a vector (a column) of x-values, then apply the function f to each x value and obtain a vector (another column) of y-values (ALERT: most mathe-maticians cringe at the application of the function f to a vector). Plot one vector (column) against the other.
Task (10 min):
Check the help for plot.
Create a plot for a function like sin or x->x^2 using 500 data points (pick your favorite function).
Expect trouble with the differences between .* and * or ./ and / or .^2 and ^2. This may take some time!
For fun try out various plot styles (like 'r-' , 'yo', or 'c*').
Prepare one presentation per team -- a team representative will be chosen at random to explain the steps.
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2. Creating matrices:
MATLAB essentially recognizes only one data structure: EVERYTHING is a matrix!
You know how to type in a matrix component-by-component.
For the graph using 500 points this was out of question -- you used ranges!
In the first class using MATLAB you learnt a few special commands like zeros, eye that make matrices.
But there are many more -- and we will need many of them! (check out hilbert, magic, meshgrid ......)
Task (10 min) (Team-to-team competition)
Find as many, essentially distinct, ways to create (usually large) matrices as possible. 12 is a good target!
Homework (due Friday, in teams):
Find even more ways -- try to get at least twenty. Bonus credit for the winning team, and for two volunteers who will summarize (for distribution to the whole class) all discoveries presented Friday.
Hints:
Except for asking MATLAB veterans (which should be properly acknowledged, and is not really fair),
your only choice is to browse the HELP INDEX. Pay attention to examples and referrals ``SEE ALSO''
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