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 What is Mathematica? It's a powerful symbolic numerical, and graphical
computer algebra system. It's a word processor with live mathematical
content. It's the hottest thing to come along since the slide
rule. And I drew these four cool pictures in Mathematica using
3D trigonometry!



 Email me your requests
for topics for more notebooks.


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 (c) 19972000 Dan
Bach and B & L Math Enterprises; all rights reserved. Download
for personal use only.


 Some Mathematica Examples
[ top of page ]


Here are some simple sample
inputs, outputs, and graphics from Mathematica:
"In" is what you
type in, "Out" is what the computer
calculates.
Challenge yourself or others
to solve more complex problems and draw amazing pictures. I do
take questions by email: dbach@dvc.edu or go to the ask dan
page.


In: 2 + 3 * 4 (* order of operations *)
Out: 14
In: N[Sqrt[2], 40] (* plenty of accuracy *)
Out: 1.4142135623730950488016887242096980785697
In: 5x^2 + 13x + 14 /. x>7/8
(* substitution *)
Out: 1869/64
In: Solve[3x + 5 == 11, x] (* solving an equation *)
Out: {{x>2}}
In: Factor[x^2  8x + 15] (* factoring a wild quadratic *)
Out: (x  3)(x  5)
In: f[x_] = x^2  8x + 15 (* defining a function *)
Out: x^2  8x + 15
In: {f[3], f[4], f[5]} (* a list of values *)
Out: {0, 1, 0}
In: Table[f[n], {n, 3, 8} (* a table is a list *)
Out: {0, 1, 0, 3, 8,
15}
In: Plot[Sin[x^2],{x,4,4}] (* some kind of plot *)
Out: 

In: Plot3D[Sin[x^2 + y^2],{x,3,3},{y,3,3}]
Out: 


If you have Mathematica
available to you, try these examples out for yourself.
See what happens when you change
the problems slightly. 


If you're
willing to add a few options, you can dramatically improve the
appearance of the pictures. Save a copy, then change things. 

In: f[x_] := Sin[x^2];
Plot[{f[x],f'[x]/4,f''[x]/20}, {x,4,4},
Frame>True, Axes>{True,False},
Background>GrayLevel[.9],
PlotLabel>"Which curve is f, f', f''?",
PlotStyle>{Hue[0],Hue[.6],Hue[.8]}];
Out: 

In: Plot3D[Sin[x^2 + y^2], {x,2,2}, {y,2,3},
PlotPoints>75, ColorFunction>Hue,
Axes>None, Mesh>False];
Out:  
Cool, huh? [ top of page ]
Dan's Mathematica History [
top of page ]

I've been involved with Mathematica since 1988, when
I tested the prerelease beta version 0.9 on a NeXT cube, at
the Mathematical Sciences Research Institute (MSRI, or "misery")
above UC Berkeley. At that time it was buggy (reporting that
the integral of 1/x from 2 to 2 was 0).
 The following year, in 1989, I convinced the college
(DVC) to purchase a working copy of Mathematica (then in version
1.2) to run on our Macintosh SE, which had to be upgraded to
4 MB of RAM to handle the task.

 From 1989 to 1991 I attended
many workshops, in Maple, Derive, Theorist, and Mathematica,
finally settling on the latter as my weapon of choice. Special
thanks to Wade Ellis, Jr. of West Valley College for this timespan.
[ top of page ]

 In the Summer of 1992 there
were eight intensive, oneweek workshops given in various
software packages, including the above. I attended one in Los
Angeles and wrote what evolved into Precalculus and Mathematica,
a series of interactive notebooks from beginning algebra and
functions through trig. Thanks to Bill Davis and Alan deGuzman
for their excellent workshops at LA Pierce College and Dearborn,
Michigan.

 I was then chosen as one
of eight national developers for the Interactive Mathematics
Text Project (IMTP), under a grant by NSF, MAA, and IBM.
I made presentations at the developers conferences at University
of Michigan (1994), St. Louis, Mo. (1995) and at the Joint National
Mathematics Meetings at Orlando, Fla (1996).

 More recently I have given
regular workshops at DVC: "Using
Mathematica Is Easy"
(for students) part of the College Success Workshops,
and Instructional Flex Workshops (for teachers in the
3college district).

 In April 1998 I gave
a talk at the Lake Tahoe Recreational Math Conference,
"See It and Hear
It in Mathematica"
about using all the senses to experience math. I expanded this
talk for an August 1998 Flex Workshop for District Faculty,
and revised the talk for the CMC^3 conference in Monterey
in early December 1998. In May 2001, I revisited
the Lake Tahoe Conference with a new talk, "Math in (at least) 3D".

 Check out the Mathematica
web site at www.wolfram.com. It has info on the current version
(4.1) and all the options and prices and stuff. Be aware of the
student version if you want a cheaper way to get into the game
(about $139).

 One cool site for you to
check out, especially if you're a calculus student, is the Mathematica
Integrator page at www.integrals.com. This lets you enter in your f(x),
sends it to their computer, figures out the integral (antiderivative),
and sends it back to your page. And you don't have to have a
copy of Mathematica to use it!


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