MTH3051 Introduction to Computational Mathematics - User Web ...

School of Mathematical Sciences
Monash University
n = 100; % set number of terms
sum = 0; % set initial value for sum
sign = 1; % an integer +/- 1
for k = 1 : n
% loop over k from 1 to n
term = sign/(2*k-1); % compute the term
sum = sum + term; % update rolling sum
sign = - sign; % flip the sign
end;
disp(n);
% print n
disp(4*sum);
% print the approximation to π
disp(4*sum-pi);
% print the error
This is an example of Matlab syntax. Matlab is a programming language well suited
to numerical computations. There are many other languages such as Fortran, C, Java,
Maple and Mathematica. They all have a similar flavour and they all serve the one
purpose of getting the computer to do useful work for us. We will use Matlab throughout
this course as it is (arguably) the easiest to learn for someone with no programming
experience. But don’t let this stop you from learning about other programming languages
(in your spare time).
In reading the above code you must keep in mind one extremely important fact the
equals sign is not what you might expect it to be. The computer will treat the equal
sign (usually) as a replacement operator. Thus in executing a line like x = 2*y the
computer will first evaluate the right-hand side then assign that value to the left-hand
side. Whatever value x had before, it will be wiped out. Its value after the line is
executed will be 2*y. This use of the equals sign allows us to write lines like x = x +
1 to increment the current value of x by 1. In contrast, if you showed a mathematician
a line like x = x + 1 he or she would look at you very very strangely (why?).
The above Matlab code is fairly easy to read. The first three lines set initial values to
various symbols (aka variables). Then we encounter a for-loop. Matlab will repeat the
code in this loop for each value of k from 1 to n in strict order. Each time through this
loop we are calculating one term in the series. After the loop finishes we print out the
various numbers that interest us (using the Matlab command disp which is short for
display ).
If the above code baffles you then one way to understand it is to pretend you are the
computer and follow the Matlab commands. Get out a pencil and paper and start
following the instructions. Work your way through the first 5 or so terms. You should
see that it is correct and does compute the series.
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