t> INTRODUCTION: WHAT IS MAPLE?
b>
t> In simplest terms, Maple is an environment for doing mathematics.
b>
t> Symbolic, numerical, and graphical computations can all be done with
t> Maple. While simple problems can be solved with Maple, its real power
t> shines through when given calculations extremely cumbersome or
t> tediously repetitive to do by hand.
b>
t> The breadth of Maple's functionality is wide - topics from calculus,
t> linear algebra, differential equations, geometry, statistics and many
t> other areas are covered. As well, Maple's coverage of these topics is
t> extensive - each area has a wealth of procedures written about it.
b>
c1> 
t> Symbolics
b>
t> Maple's symbolic routines allow you the greatest freedom. By allowing
t> variables to remain unknown (i.e., without numerical values) and in
t> exact form (e.g., 1/3 as opposed to 0.333...) throughout consecutive
t> steps of a calculation, Maple provides exact answers - with more
t> accuracy than any numerical approximation method. If a floating-point
t> result is needed, it can be calculated at the end of the computation;
t> thus, roundoff error can be avoided. Some examples of symbolic
t> manipulations follow.
b>
x> solve({a*x+b*y=1, 2*c*x+d*y=3}, {x,y});
c1>
x> int(exp(-x^2)*ln(x), x=0..infinity);
c1> 
t> Numerics
b>
t> Numerical routines provide alternative methods of solution when a
t> symbolic method would either be too slow or does not exist for a
t> particular type of calculation. Maple supports many well-known
t> numerical algorithms. All symbolic constants can be evaluated
t> numerically. Also, because of Maple's "infinite precision", numerical
t> calculations can be done to *any* number of digits accuracy. The
t> following are examples of numerical calculations.
b>
x> 5.0^(1/3);
x> sum((-1)^i*1.0/i!, i=1..20);
x> evalf(Pi, 25);
c1>
t> Graphics
b>
t> Maple's two- and three-dimensional graphics provide you with the power
t> of scientific visualization. Functions in both one and two unknowns, as
t> well as parametric equations can be represented graphically. There are
t> over twenty types of specialty plots as well as many available options
t> for customizing the way each graphic is displayed.
b>  
t> There are many examples of Maple's graphics in a following chapter of
t> this tutorial, "Plotting with Maple".
b>
c1>
t> Maple's Internal Structure
b>
t> Maple consists of three components: the kernel, the library, and
t> the interface. The kernel is the "mathematical engine" behind Maple's
t> calculations. This compact, highly optimized set of routines is written
t> and compiled in the C programming language, and performs the large part
t> of the basic computations done by the system.
b> 
t> Most of Maple's built-in procedures are written in Maple's own
t> programming language and reside in the Maple library. Code written in
t> Maple is not compiled, but "interpreted" as it is read or entered,
t> allowing you to create your own Maple procedures interactively within
t> the program.
b>
t> The interface is Maple's eyes to the world and defines, to a large
t> extent, how you interact with the commands and procedures. Depending on
t> the quality of your terminal, and the version of Maple you are running,
t> the interface may fluctuate between a "dumb" tty terminal version to a
t> sophisticated interface with Maple documents (called worksheets) 
t> containing input, output, text, and graphics.
b>
t> The remainder of this tutorial deals with issues of the kernel and
t> library, but does not explain further the various interfaces for
t> Maple. For more information on your Maple interface, refer to your copy 
t> of the "Getting Started" booklet that came with the software. 
b>
c1>
t> A Word About Semicolons and Colons
b>
t> Before we start learning in earnest, there needs to be a quick
t> explanation about command terminators. When you type in any Maple
t> statement, expression, or command, you must make sure that you end it
t> with either a semicolon or a colon. Until you do so, Maple does not
t> know that you want to calculate what you've entered, and it just
t> patiently waits for you to complete your command (no matter how many
t> lines you enter).
b>
t> The semicolon is the standard Maple command terminator. It tells Maple
t> to calculate the previous input and display the result. When a colon is
t> specified, the result is suppressed - this is particularly useful when
t> the output is bound to be too large to view conveniently or is only an
t> intermediate result towards a further end. Unless otherwise asked,
t> please use the semicolon to terminate all commands entered in this tutorial.
b>
t> (Note: As a courtesy to those who slip, if you forget to enter
t> a terminator for any command in this tutorial, one will be appended
t> for you automatically. This *will not* happen outside this tutorial!)
b>
c1>
t> Maple's Help Facilities
b>
t> Maple has an in-depth help facility that includes help files for each
t> command, data type, and construct in the Maple language and library.
t> The standard way to call up one of these help files is with the ?
t> syntax.  Simply enter the name of the command preceded by a ?
t> character, and Maple will display the help file if it exists. If no
t> such help file exists Maple will provide you with a list of other
t> possible choices to try.
b>
t> Any time during this tutorial when you are prompted for a Maple command
t> (i.e., during the Questions sections or a Quiz) you can use the ? syntax
t> to display a Maple help file. If you are running this tutorial on a
t> "dumb" (tty) terminal, the help information will be added to the flow
t> of the tutorial. If you have a more advanced terminal, the information
t> will appear in a separate help window. Make sure to close off these
t> help windows when you are finished with them or you will clutter up the
t> screen.
b>
t> The following command calls up the help screen for the command expand.
b>
c1>
x> ?expand
c1>
t> As you can see, a help file contains several different types of 
t> information, such as calling sequence, synopsis, and examples. If 
t> all this information is more than you really want, there are also 
t> several commands that return only specific parts of a help file. These 
t> commands include info, usage, example, and related. Following are 
t> examples of each for the command simplify.
b>
c1>
x> info(simplify);
c1>
x> usage(simplify);
c1>
x> example(simplify);
c1>
x> related(simplify);
c1>
t> On platforms with more advanced terminals, there is also a
t> multi-leveled help topic browser available. This browser allows you to
t> navigate through the different Maple help files more intuitively.
b>
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