LAB 1, 01/29/14
_______________

1.	Customize MATLAB workspace: DESKTOP menu

		COMMAND (window) - absolutely necessary
	
		COMMAND HISTORY - useful when repeating commands
		WORKSPACE - useful for keeping track of variables
		CURRENT DIRECTORY - listing of files
		EDITOR - for creating .M files (script and function)
		HELP - documentation

	All windows can be popped out.


2.	Assigning values to scalar variables; number formats

		x = 2;		% semicolon suppresses output

		x = 3		% note the output

		x^2		% again, note output

		ans		% most recent numerical output that
				% was not assigned to a variable; now ans

		y = pi*ans	

		format long; y 	% semicolon also implies new line

		format short e; y

		format rat; y

		format; y	% returns to default format (see HELP)

	Question: What variables appear in the Workspace window?

3.	Array variables (i.e., mxn matrices) are fundamental to all 
	MATLAB functions.  Scalar variables (introduced above) are
	special (1x1) cases of arrays.

	The elements (entries) of an array 

	- are enclosed in [ ]

	- are separated horizontally using spaces or commas

	- are separated vertically using newlines or ;

	Transposition (rows <--> columns) is accomplished
	using .' or simply ' if all entries are real.

	For example:

		vrow = [1 2 4 8] 		% row vector

		vcol = [1 
			3
			9
			27]			% column vector
	
		vcol = [1 ; 3 ; 9 ; 27]		% alternatively

		A = [1 2 4 8
		     1 3 9 27]

		A = [1 2 4 8 ; 1 3 9 27]	% alternatively

		vcol'				% note use of '

		[vrow ; vcol']			% alternative for A

		A'

		A.'				% same as ' for real A

		[vrow' ; vcol]			% same as A' ?


4.	Array indexing is simple:

	- v(k) is kth element of a row or column vector

	- A(k,l) is the (k,l)th element of a 2-dimensional matrix

	k and l can be replaced by vectors of indices (K and L),
	in which case v(K) and A(K,L) are sub-arrays of v and A.
	More on that later.

	Vectors with regularly spaced entries on the real line
	are created using an expression of the form

		FIRST VALUE : INCREMENT : LAST VALUE

	For example:

		v1 = 0 : 0.1 : 2	% what is the size of v1?

		v2 = (1 : 0.01 : 2).'	% what is the size of v2?

		v3 = 2 : -0.1 : 0	% relationship to v1?

		v4 = 0 : 0.1 : 2.05	% relationship to v1?

		v5 = 0 : 10		% see below

	If INCREMENT is omitted, then it equals 1 by default.


5.	MATLAB has powerful graphing capabilities.  Two common
	graphing commands are

		PLOT (generally used for continuous graphs)

		STEM (suited for functions of a discrete variable)

	There are several optional parameters for both commands.
	In their simplest form,

		PLOT(X) or STEM(X)

	plots the vector X against the indices 1:length(X).  

	Also,
		PLOT(X,Y)

	where X and Y are vectors of the same length, plots
	Y (vertical axis) against X (horizontal axis).


		plot(v1)		% continuous graph

		stem(v1)		% discrete graph

		plot(v1,3*v1)		% explain the result


6.	You can use either i or j (for the imaginary unit) to
	enter complex numbers - provided i and j have not 
	been previously assigned other values.

		3+4*i
		
		3+i*4

		3+j*4

		3 + j*4

		3 + 4i

		3 + 4j

		3 + j4		% unassigned variable j4

		[3 + 4j]	% 1x1 array

		[3 +4j]		% 1x2 array


7.	Naturally, if x and y are real vectors of the same size
	and orientation, z = x+j*y will produce a complex 
	vector.

	The command PLOT(Z), where z is a complex vector, plots
	the imaginary part of Z against the real part of Z.

	Transposition of complex vectors is achieved using .'

	Use of ' (without the period) will result in complex
	conjugation, as well.

		z = v1 + j*3*v1 ;

		plot(z)		% same plot as before

		v1 + j*v2 ;	% v1 and v2 not of the same size

		(3+4j).'	% 1x1, so transpose has no effect

		(3+4j)'		% complex conjugation!

		plot(z.')	% same plot as before

		plot(z')	% explain the results