With this lesson we will begin our study of Mathematica. There are a number of
reasons why Mathematica is a good place to start when learning about computer-based
engineering problem solving.
First of all, Mathematica is both extremely powerful and relatively easy to use. You
can do interesting things with Mathematica even if you are a complete beginner. Its
support for numerical computation is far more comprehensive and flexible than
is provided by a scientific calculator. And even though Mathematica is much more
powerful than a calculator, it is not really much harder to use. Before
systems like Mathematica were available, the only way to do computer-based problem
solving was to write programs (usually in Fortran or C). But with Mathematica you
can solve complex problems quickly and without doing much (if any) programming.
In order to solve the same kinds of problems in Fortran or C, you would need
much more training.
Second, Mathematica supports symbolic computation in addition to numerical
computation. You are doubtless familiar with numerical computation, which is
what you do with a pocket calculator, and is what many scientific Fortran and C
programs do. Symbolic computation involves manipulating mathematical symbols
much like you do when factoring polynomials or differentiating functions.
Third, Mathematica provides convenient facilities for visualizing your work. With
Mathematica, you can easily produce two- and three-dimensional plots. This will add
another dimension to your understanding of scientific and engineering
principles.
Finally, Mathematica is a form of programming. We will use Mathematica to illuminate a
number of concepts that will arise later when we study C and Fortran. The
background that you gain in using Mathematica will make it easier to learn these
languages.
In this and the lessons that follow, we will illuminate each of these aspects
of Mathematica.