Matlab

Matlab Tips

Taking a numerical analysis class is more or less like a 'cultural shock' to some students from pure to computer, from formulas to algorithms. Here are a few tips.

Have access to Matlab and able to open it. You can used Matlab with university license, or buy a student version with $49.99 or $99.00 (recommended).

Make sure you are working on current directory, you can use pwd in Matlab to find where you are; and use cd to change to your designed directory. I suggest that you create a directory under Desktop called MAxxx, say MA580, ... You should put all the related files in the same directory.
Check the instructor's or course web-page. I often put sample files there. You can modify them accordingly.
Often we create three type of files for one problem. The first type is define functions that involved, for example, f(x) can be put (using a text editor, included in Matlab)

function y = f(x)

y = cos(x);    % or other function

return

The file should be saved as f.m.   Warning, do not abuse the use of f.m, you can use f1.m, f2.m, f3.m ... for different function.

The derivative of the function f'(x) can be defined as

function y = fp(x)

yp = -sin(x);    % or other function

return

The function should be named as fp.m

The second type is an algorithm file, for example, if we use the forward Euler's formula, we can write

function y = feuler(x,h)    % x and h are inputs, y is the output

y = (f(x+h)-f(x))/h; % You need f.m is defined.

return

The file should be saved as feuler.m.

The third type of files are called script file, say hw1.m whose contents are
h=1; x=pi/4; k=1;

while h>1e-17                   % A conditional loop
  [et1,et2,et3] = feuler(x,h);
  e1(k) = et1; h1(k)=h;         % save the data
  k = k+1;
  h = h/2;
end

e1,             % Show the date (error)
loglog(h1,e1);  % Plot the error versus 

It's good practice to clean the house (storage) using

clear all; close all;

To create a Matlab function, make sure it has already been used in Matlab such as diff, euler, to find out using whether diff used

help diff

If it is used, you can use something like my_diff

Read a few chapters of a Matlab tutorial.
See sample Matlab code from the instructor from the notes, web-site, sum, product, Ax, Hornet (nested) method for computing polynomials.