See also Setting up the MATLAB Environment at MCSR and  Getting Started with MATLAB at MCSR, Part II

Matlab solves various equations and obtains solution for some mathematical functions. To activate MATLAB on willow or sweetgum enter: matlab. To get a flavor of what matlab has to offer enter: help after Matlab is activated. Their Web Site, www.mathworks.com, contains online help that includes instructions on how to set up and run small examples. For further information, users may check MCSR Website: http://www.mcsr.olemiss.edu/computing/matlab.html

 

Examples given below show both the strength and the simplicity of Matlab.  Matlab contains a variety of mathematical and statistical functions. Below is an example that finds the value for Error Function erfc. Please note that x is the input to the Error Function and y is the result or the output from the Error Function.

 

>> x=.78

 

x =

 

    0.7800

 

>> y=erfc(x)

 

y =

 

    0.2700

 

To find the roots of a polynomial p=x^3 -2*x -5 in Matlab, user at the Matlab prompt >>, enters:

p = [1 0 -2 -5] ; please note that numbers in bracket represent the coefficient of the polynomial.

 

To that Matlab responds by:

 

p =

 

     1     0    -2    -5

 

Then user enters: r= roots(p).

At this point the roots are printed. Here is how:

 

First Matlab is activated by entering: matlab.

 

< M A T L A B >

                  Copyright 1984-2002 The MathWorks, Inc.

                      Version 6.5.0.180913a Release 13

                                Jun 18 2002

 

 

>> p = [1 0 -2 -5]   ;;;;;;;;;;; First line entered by user after matlab is activated.;;;;;;;;;

 

p =

 

     1     0    -2    -5

 

>> r= roots(p)  ;;;;;;;;;; Second and last line entered by user. ;;;;;;;;;;;;;;;;;

 

r =         ;;;;;;;;;;Followings are the result or the roots for the above equation.;;;;;;;;;;;;;

 

   2.0946         

  -1.0473 + 1.1359i

  -1.0473 - 1.1359i

 

Please notice that one of the roots is real and the other two are imaginary as the highest power in this equation is 3, (x^3), we expect to obtain 3 roots.

 

In high school we learned how to solve simple linear equations with 2 or at most 3 variables. Users may find an example of solving linear equations with many variables at:

http://www.mcsr.olemiss.edu/appssubpage.php?pagename=imsl.inc

 

 

Also at high school they taught us how to solve quadratic equations with one variable e. g. x^2 -1=0, whose two roots are plus and minus one. The above example on this article solves this family of equations. What we didn 't learn in high school or even in the first few years of college was the combinations of the above two systems. That is a system of equations that contain several variables as well as some quadratic and cross product terms. Such a system of equations is called non-linear system of equations. When the laws of nature and the laws of physics are formulated in mathematical terms the resulting equations become messy, nasty and difficult to solve. These equations are not simple equations like x^2-1=0, and their solutions requires developing new methods which involve a lot of analysis. In our next article we see how PV-WAVE and others solve these systems of equations.

 

Users needing help with Matlab or other mathematical or statistical software should send email to assist@mcsr.olemiss.edu,.