**Welcome to the Rutgers Maple Help Pages!**

An essay on how Maple can be useful to you in your multivariable calculus class and beyond.
In this Section: |

Almost every aspect of the practice of mathematics, both pure and applied, has been improved and amplified in recent decades by the widespread availability of "computer algebra systems" (CAS). This technology is much more than just algebra, of course. It is a collection of systematic and powerful programs that permit

- What is the coefficient of
*x*^{6}*y*^{4}*z*^{2}in (*x*+*y*+*z*)^{12}?

- What is an approximation to the only root of
3
*x*+cos(2*x*^{2})=0?

- What do the points
(
*x*,*y*,*z*) which satisfy the equation*z*^{2}+(*x*^{2}+*y*^{2}-1)(*x*^{2}+*y*^{2}-2)=0 look like?

The freedom to work with "exact" symbolic computation, with numerical
approximation (with specified accuracy) and with visual display of
data (human beings learn much more from pictures than from lists of
numbers!) is very useful. `Maple`
provides an environment which allows all of these, plus the freedom to
move among these representations of mathematical ideas.

Much teaching **and** research is now improved
by access to powerful programs which allow
*experimentation*. Examples can be discovered and explored which
are useful for instruction. These programs can also be used to further
understand complicated phenomena which are not easily explained.

**Computer help**

Many students have graphing calculators. These are useful, but are
limited by speed and memory size. Simple
errors may occur. There are large computer programs with powerful
numerical, symbolic, and graphical capabilities. These still may have
the potential for errors (as some of the contents of the link
discuss) but much effort has gone into their programming. The most
widely distributed programs are ** Maple**,

**How to get those answers**

The answers to the questions above were obtained with the following
`Maple` instructions. Please: these instructions are **not**
given to impress you, but rather to show how easy is is to get the
answers.

`coeff(coeff(coeff((x+y+z)^12,x^6),y^4),z^2);`

The command`coeff(P,monomial)`finds the coefficient of the monomial in the expression`P`. Layering three repetitions of`coeff`finds the desired coefficient.`fsolve(3*x+cos(2*x^2)=0,x);`

`fsolve`is a general "floating point" approximate equation solver. Care must be used if there's more than one root. There are also symbolic solvers, useful when there is a nice formula for the solution.`with(plots):`

V:=((x^2+y^2)-1):

W:=((x^2+y^2)-2):

implicitplot3d(-V*W=z^2,x=-2..2,y=-2..2,z=-2..2,grid=[30,30,30],axes=normal);

The`implicitplot3d`command sketches graphs which are defined implicitly by equations. Since`Maple`has so many functions and libraries available, many need to be specifically loaded before use. The command`with(plots);`loads a variety of plotting commands. The`implicitplot3d`command has a wide variety of options. The`grid`option gives control over the spacing of sample points. Of course increasing the number of sample points "costs" computational time and storage space but does given finer detail.

**Programming in Maple**

*Last modified 1/11/2015. Suggestions for corrections or additions
should go to the math 251 coordinator or the math department
computer coordinator. As of Spring 2015 these are
Speer (speer@math) and Cherlin (cherlin@math).
*