As you'll soon learn, when you use Fortran or C to solve a problem, the first
step is to write out a complete list of instructions, or commands for the
computer, called a program. This program is generally stored in a file.
How is this different from the way we've been using Mathematica?
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When you use Mathematica, you type in your commands and Mathematica carries out your
instructions directly. You get the results right then, and you don't have to
decide upon all of your commands ahead of time. You can decide what you want
to do as you go along.
But when you use Fortran or C, you don't enter your commands one at a time and
the computer doesn't carry out your commands as you type them in. Instead, you
have to ``plan ahead'' and write down every command before the computer will
start carrying out any of your commands. And you have to go through some
extra intermediate steps to get the computer to carry out your program at all.
What a bother! Mathematica seems so simple and straightforward, and writing programs
seem to be so complicated! So why does anybody write complete programs at all?
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Let's look at some of the advantages to writing programs.