Miscillaneous Matlab Goodies!

On ezplot and fplot:

These are two Matlab commands that plot symbolic functions. For fplot the user must specify a vector [xmin xmax], and it is optional for ezplot. The standard way of use (with versions 4.0 and 5.5) is:

ezplot('sin(x)')

or

fplot('sin(x)',[-5 +5])

ezplot sin(x) or ezplot(y) also work if we first define y = 'sin(x)'; however, ezplot y does not work.

Defining functions symbolically:

Older version of Matlab Symbolic Toolbox (e.g., v.4.0) restricted the definition of symbolic functions according to, e.g., :

y='tanh(x) + x^2'

y =

tanh(x) + x^2

This also works with newer versions. However, newer versions (say v5.0) also allows:

syms x

y = tanh(x) + x^2

One can use findsym(y,1)to find the Matlab assumed variable in expressions containing more than one symbol. E.g.,

findsym('a*c+5',1) returns c as the variable (since c is closer to the default variable 'x').

funtool:

This is a nice Matlab command that open a user friendly interface and allows for symbolic functions (two functions of one variable each) to be plotted, differentiated, composed, etc.) funtool work from within a Matlab window.

Base Conversions:

dec2bin(45)

ans =

101101

dec2hex(45)

ans =

2D

bin2dec('10010')

ans =

18

hex2dec('E6')

ans =

230

Computing factorial and combinations:

There is no build-in function for factorial(n) in Matlab (e.g., 4! does not work). However, one can use:

prod(1:4)

ans =

24

prod(1:0)

ans =

1

or gamma(n+1) for n!

gamma(4+1)

ans =

24

Example: Find the combination C(5,3):

C=prod(1:5)/(prod(1:5-3)*prod(1:3))

C =

10

Special Variables:

pi

ans =

3.1416

Infinity: inf

eps

ans =

2.2204e-016

i

ans =

0+ 1.0000i

e.g.,

e=exp(1)

e =

2.7183