- Sections 5, 6, and 7 will meet in
**IML 119**which is*inside*the ARC computer lab. Please go there at your regular class times:- Section 5: 8:40-10:00 AM
- Section 6: 10:20-11:40 AM
- Section 7: 12:00-1:20 PM

- Sections 8, 9, and 10 will meet in
**IML 118**which is*inside*the ARC computer lab. Please go there at your regular class times:- Section 8: 12:00-1:20 PM
- Section 9: 1:40-3:00 PM
- Section 10: 3:20-4:40 PM

General introduction |
1/6/2006 |

Playing with arithmetic |
1/6/2006 |

Playing with algebra |
1/6/2006 |

Playing with calculus |
1/6/2006 |

Playing with graphs |
1/6/2006 |

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**Why learn Maple?**

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.

Almost all of my teaching **and** research is
now improved by access to powerful programs which allow me to
*experiment*. I can get examples which are useful for
instruction. I've also used these programs to try to understand
complicated phenomena which I could not easily explain.

**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, 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.

**Programming in Maple**

I have several books on `Maple` programming. My current
favorite is *Maple A comprehensive introduction* by Roy
Nicolaides and Noel Walkington, Cambridge University Press ($65, 484
pages, available for less in places on the web). There are also many
web pages which discuss programming in `Maple`. For example,
here's one
online tutorial. Warning: such pages are only for the enthusiast!

**
Maintained by
greenfie@math.rutgers.edu and last modified 1/6/2006.
**