Important points:

• MATLAB is case sensitive

• On-line HELP is available as follows:

>>  help (gives categories)
>>  help elfun  (elementary functions, from the help command above)
>>  help sqrt

• Array operations take place on an entry-by-entry basis. In the example below, X .* Y is an array operation:

 >>  X = [2 3 4]; Y = [1 2 3];

>>  X .* Y

ans =

2 6 12

• The expression X * Y’ is a matrix operation; it is defined according to the rules of linear algebra.  The ' symbol is the transpose operator.

 >>  X * Y'

ans =

20

• The semicolon separator has two purposes. You can put multiple MATLAB commands on a single line. This makes M-files especially compact. At the end of a line, the semicolon supresses the normal display of the answer you have requested. Examine the difference between:
 

expanded form	abbreviated form
>>  a=2	>>  a=2; b=3;
>>  b=3

• M-files contain general MATLAB statements. This way, a particular sequence of operations can be pre-programmed and stored. This is very similar to programming in BASIC or other mathematical languages.

• Functions are specific mathematical functions stored in separate files.

• Executing commands can be stopped by entering control-C
 
 

EXAMPLES

1) Simple computations, operators, and functions
 

>>  2+2	>>  sin(2*pi*3)
>>  2*3-7/4	>>  log (42) * exp(4.4)
>>  a=3; b = 9
>>  log(a^sqrt(b/2))	>>  3*a^2+4*b^3

2) Working with arrays

Determine which operations below will compute, and why.
>>  t = [ 1 2 3]; u = [ 4 5 6] ; w = [ -2; 1; 4];
>>  t + u
>>  4 * t - 2 * u
>>  t * u
>>  t .* u
>>  v = t'
>>  t * v
>>  u * w
>>  w + 2 * v
>>  m = [t; y]
 

3) Arrays used for function plotting

Define an array of independent variable values: t(1) = 0, t(2) = .1, . . . t(21) = 2

>>  t = [0 : .1 : 2 ]

Define an array of dependent values: y(1) = 3*(0)^2 - 4*(0) + 7 = 7, y(2) = etc., ..., y(21) = 3*(2)^2 +4*(2) +7

>>  y = 3*t  .^  2 - 4 * t + 7 (Notice the .^ operator)

Plot y as a function of t:

>>  plot (t,y); xlabel(‘t’); ylabel(‘y’); title(‘A polynomial plot’)

An alternate way to define the t array

>>   t = linspace(0, 2, 21)
 

4) Working with complex numbers
>>  sqrt(-3)
>>  x = 3+2i
>>  real(x); imag(x)

Determine the roots of the polynomial 1x² - 2x + 3 = 0

>>  roots([1 -2  3])