Math Software For MITx 6.002x

[HLA-27b]

As MITx 6.002x started to get into more involved maths I thought to show you a few basic math programs (in case you didn't know them already) which might help.

The first is Microsoft Mathematics (yes I know  but it is free!)
This is basically a graphing calculator and equation solver with some flair and it is mostly intended for high school students.


What you see on the image is me solving S6E2: Load Line exercise.
The first equation (blue) is I=V^3 given in the exercise. Since the graph recognizes only x and y they are substituted y for I and x for V hence y=x^3

The second one (green) does not look like much but the basic idea is that this is a straight line with a slope. The formula for a line with a slope is
y=mx+b where

y is the vertical axis (Amps)
m is the slope (Agraval gives this in the book as being equal to -1/R and since R is 8.2 ohms I enter -1/8.2 and the program then "simplifies" to -5/45)
x is the horizontal axis (Volts)
b is the y-intercept point i.e. where the line intercepts the y axis
the formula I looked up from here, I don't memorize this sort of stuff.

Unfortunately MS Maths does not have a cursor per se so you have to punch in yet another formula to get the intersection point of the two lines. Instead of doing that you can as well get the Graph 4.3 which is free and open source and does the graphing exceedingly better but does not have a calculator or equation solver.

Notice how the cursor is set to snap to the intersection and the coordinates show the solution of the problem. Entering of the formulas is not as easy on this one but you can always "copy special" from MS maths. In any case you should allow an hour or two to learn to talk to these programs properly.

Hope these encourage a few folks to stick to the course, it is disheartening to see people dropping off.

[Randall W. Lott]

Fantastic work.  I'll be trying this out when I get a chance.

[Lightages]

Also worth looking at and free:
http://www.gnu.org/software/octave/
http://www.scilab.org/products/scilab
http://hp.giesselink.com/emu48.htm

and FYI, I love RPN!

[sonicj]

OSX has what appears to be a pretty nice graphing application bundled with the OS. ( /Applications/Utilities/Grapher )  I can't figure out how to snap to the intersection though.... 

[Andy]

I'm getting by just using wolfram alpha: http://www.wolframalpha.com/

[HLA-27b]

Also worth looking at and free:
http://www.gnu.org/software/octave/
http://www.scilab.org/products/scilab
http://hp.giesselink.com/emu48.htm

and FYI, I love RPN!

Many math packages seem to be based on Maxima code. Octave(not this one), Euler, GeoGebra, SAGE etc. Unfortunately they either depend on RPN infix + special syntax or in the case of GeoGebra have a specialized graphical interface. I'm not a big fan of RPN or infix notation - all I want is a sleek natural math interface like in the books + graphing + unit converter + math books (a la SpeedCrunch) + spreadsheet all in one (not much eh?). Unfortunately there are none that I know of.

Btw, SpeedCrunch is the ultimate replacement for a scientific calculator. Use it people its great.

OSX has what appears to be a pretty nice graphing application bundled with the OS. ( /Applications/Utilities/Grapher )  I can't figure out how to snap to the intersection though.... 

It goes to show that those who write the programs don't know how to use'em
 Graph can run on OCX with a windows emulator, or so it says at least.

[alm]

Octave is based on Maxima? Octave is a numerical package (MATLAB clone), so I find this very unlikely. It may depend on Maxima for symbolic operations, like MATLAB used to depend on Maple for its Symbolic Toolbox, but I wouldn't expect much need for symbolic features in a sophomore EE course. The same applies to Scilab, which is another MATLAB clone, but with some different features and with a slightly different syntax.

SAGE is basically all open-source math packages put together, so it does include Maxima, but it can also use some other symbolic and numeric backends. Not something I would recommend for some quick calculations, however.

None of these packages use RPN, although they're not an attempt to emulate a traditional calculator on a computer, something that doesn't make much sense in my opinion. I can type number, operators and functions just fine with the keyboard, instead of manipulating a smaller number of keys with my mouse.

[HLA-27b]

Octave is based on Maxima? Octave is a numerical package (MATLAB clone), so I find this very unlikely. It may depend on Maxima for symbolic operations, like MATLAB used to depend on Maple for its Symbolic Toolbox, but I wouldn't expect much need for symbolic features in a sophomore EE course. The same applies to Scilab, which is another MATLAB clone, but with some different features and with a slightly different syntax.

You are right of course. I assumed Octave used Maxima code because it was listed here
Apparently I misunderstood the heading "Other Open Source Mathematical Software" as "Other Open Source Mathematical Software using maxima" I stand corrected.

SAGE is basically all open-source math packages put together, so it does include Maxima, but it can also use some other symbolic and numeric backends. Not something I would recommend for some quick calculations, however.

None of these packages use RPN, although they're not an attempt to emulate a traditional calculator on a computer, something that doesn't make much sense in my opinion. I can type number, operators and functions just fine with the keyboard, instead of manipulating a smaller number of keys with my mouse.

No its not RPN, you are right again, more like infix notation or BASIC notation.  On my keyboard (laptop Tr-Q) I can not  type even ^ without using AltGr combination and I am absolute rubbish at memorizing those. I prefer to have buttons for ^ sqrt and the like. To me, if its not in standard math notation like in the books it only adds to the confusion.

[sonicj]

It goes to show that those who write the programs don't know how to use'em
 Graph can run on OCX with a windows emulator, or so it says at least.

PEBKAC error!    I found it! 

[robrenz]

I use my sons student license of Maple.  Very nice! it lets me do things I could not begin to do without it. I know just enough to be dangerous but it does all the heavy lifting.

[slateraptor]

Btw, SpeedCrunch is the ultimate replacement for a scientific calculator. Use it people its great.

Quiet yourself, heathen. What you speak of is blasphemy!



FOREVER***!

*** ...or until HP releases another RPN scientific calculator that's better.

[harnon]

Freemat is another Matlab alternative http://freemat.sourceforge.net/
And Smath is a Mathcad alternative. http://smath.info/wiki.

I havent used either extensively but they look interesting.  Wolfram is amazing for double checking some calculus or algebra.

[slateraptor]

We're still talking about 6.002x here...right? Why would a student need anything more than paper, pencil, and a decent scientific calculator?

Or has the discussion simply shifted to free math software?

[McMonster]

A student really only needs a pen and paper. Scientific calculators are handy when you have to plug in some real life values, but teaching can be done by picking values in a way that you can calculate it quickly on paper or in your head without any harm to the teaching process itself. Relying on those fancy calculators can in some cases harm student's understanding of calculations themselves. How can you rely on your math when you only put the values into a computer and get your result all the time? Can be handy if you're in the middle of nowhere without your electronic gadgets or simply too lazy to walk across the room to get them.

[slateraptor]

A student really only needs a pen and paper. Scientific calculators are handy when you have to plug in some real life values, but teaching can be done by picking values in a way that you can calculate it quickly on paper or in your head without any harm to the teaching process itself. Relying on those fancy calculators can in some cases harm student's understanding of calculations themselves.

For e^x, carefully select a value for x that does not contain a natural log such that e^x can be easily evaluated with paper and pencil.

For sin(x) or cos(x), evaluate either function for any non-zero integer x using paper and pencil.

Learning symbolically has its place (a very important one), but engineers must also dive into practical design, which is all but impossible without numerical evaluation. At this level of academics, I don't see how scientific calculators can impede the learning process; in fact, most of my peers think I'm crazy for allowing myself the disadvantage of walking into exams with a mere 35s. A graphing calculator with symbolic capability is unnecessary, not so much a basic scientific calculator.

[harnon]

We're still talking about 6.002x here...right? Why would a student need anything more than paper, pencil, and a decent scientific calculator?

Or has the discussion simply shifted to free math software?

What is the difference between free maths software for engineering and free maths software?

[slateraptor]

What is the difference between free maths software for engineering and free maths software?

Besides the obvious functionality that engineering-specific software caters to, how about its relevance as a tool to aid in the successful completion of 6.002x.

[McMonster]

Learning symbolically has its place (a very important one), but engineers must also dive into practical design, which is all but impossible without numerical evaluation. At this level of academics, I don't see how scientific calculators can impede the learning process; in fact, most of my peers think I'm crazy for allowing myself the disadvantage of walking into exams with a mere 35s. A graphing calculator with symbolic capability is unnecessary, not so much a basic scientific calculator.

That's basically what I mean, I was speaking more in general. But I do have a feeling that 6.002x has a bit too many "type into your calculator" exercises. Playing with real numbers is important, but using a calculator requires little effort and practice.

[jgbena]

Btw, SpeedCrunch is the ultimate replacement for a scientific calculator. Use it people its great.

Quiet yourself, heathen. What you speak of is blasphemy!



FOREVER***!

*** ...or until HP releases another RPN scientific calculator that's better.

Ahhhh, put that on the pedestal next to my HP41!!!