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[ some examples . . | . . options for graphics ]
 
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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!
 
 
E-mail me your requests for topics for more notebooks.
 
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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 e-mail: 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 pre-release 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, one-week 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 3-college 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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