Engineering Applications of Computer Algebra: Mathematica Approach

Dr. Cetin Cetinkaya
Wolfram Research, Inc.
(217) 398-0747
Fax   : 217-398-0747
E-mail: cetin@wri.com

In every stage of engineering design and analysis process,  a large
amount of mathematical operations is performed.  Governing equations of
a physical phenomenon are manipulated to transform them into solvable
forms by employing approximations and simplifications techniques. In
generating a modern design for today's competitive markets, the
accuracy and precision of operations performed in this stage are
extremely important. To ensure that the resulting equations -model-
accurately represent the physical system under consideration, modeling
and analysis process requires a strong understanding of mathematical
operations from various branches of mathematics and access to various
analytical tools.  Also, since these computations are highly tedious
and repetitive to perform by hand, a user- friendly system which can
efficiently perform mathematical operations is needed.

The ideal system should let the user to concentrate on the mental
aspects of the engineering process while the computer performs the
routine mathematical operations accurately not only on numbers, but
also on symbolic quantities (expressions).  Such a system should
provide the user with a large collection of reliable and stable tools
(functions). The user should not spend too much time in remembering
standard formulas or searching the pages of handbooks and reference
books.  Facilities for clear representation of the output, such as
graphics and sound are also quite desirable. These needs along with the
advent of the computer industry (both software and hardware technology)
brings a new breed of computer systems into the engineering
marketplace.

In this paper, the technical computations environment Mathematica and
its interface the Mathematica front-end are presented with various
examples.  The symbolic capability of Mathematica and its relevance to
engineering analysis and education are emphasized.  The systematic
documentation with Mathematica notebooks and the communications
protocol Mathlink to other engineering software are also discussed. In
the light of these capabilities of Mathematica, its use in engineering
and engineering education is examined.