Math 320 — Using your Computer

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Graphing Calculators

Occasionally you will have to graph a function. Before grabbing a piece of electronic equipment use your brain & education and try to make a rough sketch of the graph. E.g., if you have to graph y=e^-xsin(2x), first ask your self “what does the graph of sin(2x) look like?”; then think what multiplying with e^-x does to that graph. If that doesn't give you anything, try again. Then, if you want a carefully drawn picture use your graphing calculator, or type the function into a graphing pogram on your computer. Here are some options:

If you have a Mac, then open grapher.app. This program is in the utilities folder which sits in the Applications folder on your computer. The program is pretty self explanatory, but there is a tab with demos that you can look at.

If you're running a Windows machine, you can download a free graphing calculator from this link. It does what it says, namely it graphs functions in 2D and 3D.

Using Octave/Matlab

Octave and Matlab are very commonly used software packages which can do matrix computations for you. If you are seriously going to use Octave/Matlab you should install either of them on your computer. Octave is free and not very hard to install.

To install Octave on your computer (Windows or Mac) visit http://octave.sourceforge.net/ and click on either “Windows installer” or “Octave.app for Mac OS X” depending on your OS.

Instead of installing software on your computer you can go to this website where you can enter a few lines of Matlab/Octave code, and immediately get the result. This will work well enough for the homework problems. There is a short tutorial on the Math Calculator site. On wednesday I will show how to use the site by running these Octave snippets

Plotting solutions of Differential equations

The Virtual Math Museum has a Java applet which will draw slope fields of a differential equation, and also plot solutions through any initial value you specify with the click of a mouse.

Reduced Row Echelon Forms

Finding the Reduced Row Echelon Form (“rref”) of a matrix is an operation that computers are much better at than humans, at least as long as the matrix contains explicit numbers. If the matrix contains variables (k, λ, …) then the machine's advantages over us are not as large.

§3.3, page 175 of our book shows some options.

If you have graphing calculator like the TI-84, then you can find the RREF of matrices with the push of a button. Or, quite a few buttons actually. There is an 8 minute youtube video which shows you how to do this. The book (page 175) tells you how to use a TI-89.
Matlab or Octave. Matlab is the industry standard tool for scientific computation. There is a free counterpart called Octave. Either of these software packages will allow you to find reduced row echelon forms, matrix products, inverses of matrices and much more. Once we have covered more material, I will post information here on how to use Octave/Matlab, and give a brief demo in lecture.
Python & Numpy. If programming is in your future, then there's a fairly easy to learn language called Python which, when combined with the package “Numpy” can be used to perform the same matrix computations that Matlab/Octave do.

The machine has got to be accepted, but it is probably better to accept it rather as one accepts a drug — that is, grudgingly and suspiciously. Like a drug, the machine is useful, dangerous, and habit-forming. The oftener one surrenders to it the tighter its grip becomes. –George Orwell, novelist (1903–1950)