Environmental Engineering Reference
In-Depth Information
Linear algebra is the name of the mathematical field in which calculations with
matrices are treated. Some basic terms are listed in the appendix of this chapter.
While MATLAB
was designed for numerical linear algebra in the beginning, it
has become a tool for all types of mathematical calculations in the meantime.
Nowadays, MATLAB
®
has been applied in nearly every field of scientific or
technical calculations. In the academic branch there is almost no university where
MATLAB
®
is not available.
With MATLAB
®
innumerable types of mathematical operations can be
performed. Of course, numerous linear algebra calculations are available, such as
inversion of matrices, eigenvalue and eigenvector determination, which can be
applied to perform various tasks, for example, the solution of systems of linear
equations. One may perform basic statistics, numerical differentiation and integra-
tion, evaluate all types of functions, solve dynamical systems and partial differen-
tial equations, estimate parameters and so forth. All this is part of core MATLAB
®
,
®
a collection of basic mathematical tools.
5
Before some details of linear algebra are examined, an introduction into the
work with MATLAB
is necessary. This should be read by novices, but can be
skipped by those who have already worked with the program.
®
1.2.1 Getting Started with MATLAB
®
When MATLAB
is opened, the user obtains a graphical user interface on the
display, as it is shown in Fig.
1.2
, containing several windows. The main window,
to start with, is the 'Command Window', where commands are given and answered.
In the command window the MATLAB
®
' stands at the position where
the user command is shown on the display, during and after entering.
In order to start type the command:
prompt '
>>
®
Press the return button and the program gives an answer, here with the informa-
tion that a variable
a
was created in the machine containing the value
2
:
A new prompt appears after the answer of the system, in order to enable the user to
give the next command. Note that only the line after the last prompt in the command
window can be used for a new command. The former lines remain in the command
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Core MATLAB
can be extended by numerous toolboxes for special purposes, for details see:
http://www.mathworks.com/products/
. Most interesting for environmental modelling, as it is
treated here, are the optimization toolbox and the partial differential equations toolbox.
®
