Massachusetts Institute of Technology
			6.003:Signals and Systems -Fall 1998
				Matlab Picocourse 
			   exerpts from the " picocrse demo"
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%%%%%%%				Introduction
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     MATLAB is a specialized software system for
numerical computations with matrices.  We will see that
very sophisticated functions and computation routines
can be built from the basic matrix operations within 
MATLAB.     
     This 2-hour "Pico"-Course consists of a series of brief 
lessons intended to introduce the syntax of MATLAB and 
especially to present some commonly used functions
and techniques.  In addition, some very specific topics
useful for 6.003 are discussed in more detail.
     We *strongly advise* that the student becomes accustomed
to plotting capabilities, Help features, and
defining one's own specialized functions using M-files
in MATLAB.  With this goal in mind, we close our presentation
by using the power of MATLAB to analyze the step response for
the parallel RLC circuit.

     The overall presentation consists of five lessons:  

Lesson 1:  Generating Matrices
Lesson 2:  Basic Operations: Matrix and Element-wise
Lesson 3:  Working with Complex Numbers and Polynomials
Lesson 4:  Plotting and Printing
Lesson 5:  Illustrative Example -- Parallel RLC Circuit
	   (Using MATLAB Help features and defining one's own 
	    Scripts/Functions using M-files)
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%%%%%%%			 Lesson 1: Generating Matrices
%_____________________________________________________________________________
% 1) Basic syntax for defining matrices, vectors, and scalars
% 2) Some special functions: "colon" operator,"linspace","eye","zeros","ones"
% 3) Extracting elements, vectors, and blocks from existing matrices
%
% At every keypress, one or more MATLAB commands is executed and an
% explanation will follow the format below:

(Actual MATLAB syntax)		%(brief explanation of the command)

(MATLAB's response to the issued command)
%_____________________________________________________________________________
A = [1 7; -4 8]		 %2x2 matrix
A=

%___________________________________________
b = [9; 3]		%2x1 column vector
b =

%___________________________________________
c1 = [9 3]		%1x2 row vector
c1 =


c2 = b'			%1x2 row vector -- via transpose
c2 =
%___________________________________________
alpha = 1		%scalar
alpha =
%___________________________________________
H = [A b]		%2x3 matrix -- via block form (DIMENSIONS!)
H =


%___________________________________________
t1 = [0:4]		%1x5 row vector -- via "colon"

t1 =
%___________________________________________
t2 = linspace(0,4,5)		%1x5 row vector -- via "linspace"

t2 =
%___________________________________________
t3 = [-1:0.2:0]			%6x1 row vector -- via "colon"  

t3 =

t4 = linspace(-1,0,6)		%6x1 row vector -- via linspace

t4 =

%CAn also DO indescending order : [0:0.2:-1] and linspace(0,-1,6)
%___________________________________________
I1 = [1 0 0; 0 1 0 ; ...
     0 0 1]

I1 =



I2 = eye(3)			%3x3 Identity Matrix -- via "eye"

I2 =

%___________________________________________
Z1 = [0 0 0; 0 0 0]		%2x3 zero matrix

Z1 =

Z2 = zeros(2,3)			%2x3 zero matrix -- via "zeros" 

Z2 =
%___________________________________________
O2 = ones(3,2)			%3x2 ones matrix -- via "ones"

O2 =

%___________________________________________
txt = 'string'		%Can also generate matrices/vectors of characters

txt =

txt = ['s' 't' 'r'; 'i', 'n', 'g']	%Character-by-character example, 

txt =

%___________________________________________
[numrows,numcols] = size(H)	%Getting dimensions of existing variables

numrows =

numcols =

numrows = size(H,1)		%Getting number of rows only
numrows =


numcols = size(H,2)		%Getting number of columns only
numcols =
%___________________________________________
A				%Extracting elements from existing matrices

A =

     1     7
    -4     8

alpha = A(1,1)			%scalar, upper-left element of A

alpha =

%___________________________________________
H				%can use the "colon" operator

H =

     1     7     9
    -4     8     3

A = H(1:2,1:2)			%2x2 matrix block, upper-left block of A

A =

     1     7
    -4     8

b = H(1:2,3)		%2x1 column vector, top of 3rd column of A

b =
%___________________________________________
A= H(:,1:2)		%2x2 matrix block, all rows of left twp columns of H

A =

F = H(:,[1 3])		%2x2 matrix block, 1st & 3rd columns of A

F =

%___________________________________________
%can use the "size" function

A = H(1:size(H,1),1:2)	%2x2 matrix block, all rows of left twp columns of H

A =

%___________________________________________