3
> y = [ 0.08
0.015
0.009
0.006
0.0055]
Entering the name of the variable retrieves its current values. For instance:
> x
> y
We can plot data in the form of vectors using the plot command:
> plot(x,y)
This will produce a graph with the data points connected by lines. If you would prefer that the
data points be represented by symbols you can do so. For instance:
> plot(x,y,’*’)
> plot(x,y,’o’)
> plot(x,y,’.’)
Data as a Representation of a Function
A major theme in this course is that often we are interested in a certain function
y
=
f
(
x
), but
the only information we have about this function is a discrete set of data
{
(
x
i
, y
i
)
}
. Plotting the
data, as we did above, can be thought of envisioning the function using just the data. We will ±nd
later that we can also do other things with the function, like di²erentiating and integrating, just
using the available data. Numerical methods, the topic of this course, means doing mathematics by
computer. Since a computer can only store a ±nite amount of information, we will almost always
be working with a ±nite, discrete set of values of the function (data), rather than a formula for the
function.
Built-in Functions
If we wish to deal with formulas for functions,
Matlab
contains a number of built-in functions,
including all the usual functions, such as
sin( )
,
exp( )
, etc.
. The meaning of most of these is
clear. The dependent variable (input) always goes in parentheses in
Matlab
. For instance:
> sin(pi)
should return the value of sin
π
, which is of course 0 and
> exp(0)
will return
e
0
which is 1. More importantly, the built-in functions can operate not only on single
numbers but on vectors. For example:
> x = linspace(0,2*pi,40)
> y = sin(x)
> plot(x,y)