As more and more high quality software apps are appearing for the TI-83 Plus calculator, I have begun to wonder if there is anything that these amazing devices cannot be programmed to do! I must confess, one of my wish-list items for a long time now has been some computer algebra capabilities: I suppose I have been guilty of a little computer algebra-envy after using the wonderful and very powerful TI-89 and new Voyage™ 200. My enquiries to Texas Instruments, however, have been firm: no, there are no plans to develop symbolic algebra for the 83 Plus. A little disappointed by this, I decided to take matters into my own hands.
The nice people at Detached Solutions (http://www.detachedsolutions.com) have written some wonderful Apps for the 83Plus, including one called Symbolic. As the name implies, this adds basic symbolic algebra capabilities to the 83 Plus: in particular, a SIMP command to perform simplification and expansion of algebraic expressions, and a symbolic differentiation command, D. These functions operate on string variables: i.e. they require inverted commas around the input. This makes them a little awkward to use, and the output tends to look a little messy.
Fortunately, when combined with another App, called PrettyPrint (also available from DetachedSolutions but written by SoftTheiss at http://www.softheiss.com) this problem disappears. PrettyPrint does what it promises and presents algebraic expressions in correct formatting, making it easy for students at all levels to interpret their algebraic output.
These two apps can work seamlessly together, but to make the process even easier, I wrote a couple of TI-BASIC programs which offer a simple front-end for teachers and students who would like to add some alg capabilities to their 83 Plus calculators.
ALG83 takes an expression (or allows the user to pick up whatever is in Y1), presents it correctly and then offers a choice of options: simplify (or expand), substitute a value, differentiate or view the function using table of values or graph. It also links directly with a second program for equation solving.
EQNSOLV takes the left-hand and right-hand sides of an equation (or uses Y1 and Y2 if desired) and offers the choice of a “fast solve” (using the in-built SOLVE command, or a step-by-step linear equation solver.
In the example shown, the first step would be to SIMPLIFY, expanding the left-hand side. From the menu shown, choosing 2 produces a simpler form.
Next step involves, perhaps, taking 3x from both sides, so the user enters –3X.
This is automatically simplified to give the next step of the process. In this way, students may work through the equation solving process, supported by the software until they are capable of working unassisted.
So what algebra did you want to be able to do with your high school students: simplify, expand, substitute, solve equations, even some calculus? It is all here. Have fun!
Email me at steve.arnold@tpg.com.au with comments or suggestions, and visit http://www.detachedsolutions.com to download the FREE apps available there.
For comments & suggestions, please e-mail Steve Arnold.
