TI-89 series
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The TI-89 and the TI-89 Titanium are graphing calculators developed by Texas Instruments.
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The original version: TI-89
The TI-89 is a graphing calculator developed by Texas Instruments (TI) in 1998. Possessing a 160×100 pixel resolution LCD screen with advanced flash memory, coupled with TI's Advanced Mathematics Software, the TI-89 is dwarfed only by its larger and slightly more powerful cousin, the Voyage 200. Since the summer of 2004, though, the standard TI-89 has been replaced by the improved TI-89 Titanium.
The heart of the TI-89 is the Motorola 68000 microprocessor, which, depending on the calculator's hardware version, nominally runs at 10 MHz or 12 MHz. Texas Instruments has allocated 256 KB of the total RAM for the unit (190 KB of which are available to the user) and 2 MB of flash memory (700 KB of which is available to the user). The RAM and Flash ROM are used to store expressions, variables, programs, tables, text files, and lists.
User features
The TI-89 is essentially a TI-92 Plus with a limited keyboard and smaller screen. It was created partially in response to the fact that while calculators are allowed on many standardized tests, the TI-92 was considered a computer due to the QWERTY layout of its keyboard. Additionally, some people found the TI-92 unwieldy and overly large. The TI-89 is significantly smaller. It has a flash ROM, a feature present on the TI-92 Plus but not on the original TI-92. The TI-89 is not permitted on the ACT, although it is permitted on the SAT examinations.
The major advantage of the TI-89 over lower-model TI calculators is its built-in Computer Algebra System, or CAS. The calculator can evaluate and simplify algebraic expressions symbolically. For example, (x^3-x^2-8x+12)/(x+3) returns <math>x^2-4x+4<math>. The answer is pretty printed; that is, it is returned as it would be written on paper, as opposed to how it would appear on a computer. The previous answer would appear as it was displayed here, with the exponents being superscripts, instead of as x^2-4x+4.
To simplify the answer further, the factor function can be used. Entering factor((x^3-x^2-8x+12)/(x+3)) returns <math>(x-2)^2<math>. The TI-89 can also expand factored expressions; entering expand((x-2)^2) yields <math>x^2-4x+4<math>. Expand will also do partial fraction decomposition if necessary, such as in the case of expand((x-3)/(x^2-4x-12)), where it returns <math>\frac{5}{8(x+2)}+\frac{3}{8(x-6)}<math>. The calculator has two more very useful functions to simplify expressions: comDenom and propFrac. comDenom returns an answer with only one denominator; for example comDenom(x/2+(y^2-6)/3-z^2/8) returns <math>\frac{12x+8y^2-3z^2-48}{24}<math>. propFrac divides two expressions; an example would be propFrac((x^2-5)/(x-3)) returning <math>\frac{4}{x-3}+x+3<math>.
The calculator can evaluate trigonometric expressions to exact values. For example, sin(60°) returns <math>\frac{\sqrt{3}}{2}<math>. The calculator automatically reduces many trigonometric expressions; for example, sin(x)^2-1 equals <math>-(cos(x))^2<math>. It even handles expressions such as sin(arctan(x^2-6)), returning <math>(x^2-6)\sqrt{\frac{1}{x^4-12x^2+37}}<math>. The tExpand function expands things such as sin(3x)cos(x) into <math>4sin(x)(cos(x))^3-sin(x)cos(x)<math>. The tCollect function does just the opposite, reversing the expansion done by tExpand.
One of the most powerful features of the TI-89 is the solve function. It takes two arguments, the equation and the variable to be solved for. For example, solve(3x+3=12,x) returns <math>x=3<math>. For equations such as quadratics where there are multiple solutions, it returns all of them. For example, solve(x^4-x^2+3=6,x) produces <math>x=\frac{\sqrt{2(\sqrt{13}+1)}}{2} or x=\frac{-\sqrt{2(\sqrt{13}+1)}}{2}<math>. For equations with infinite solutions, it solves them by introducing arbitrary constants. For example, solve(tan(x+2)=0,x) returns x=@n1<math>\pi<math>-2, with the @n1 representing any integer.
The TI-89 can also solve systems of equations. Entering in solve(x+y=4 and x^2-6x+3=y,x) gives <math>x=\frac{\sqrt{29}+5}{2}<math> and <math>y=\frac{-\sqrt{29}-3}{2}<math> or <math>x=\frac{-\sqrt{29}-5}{2}<math> and <math>y=\frac{\sqrt{29}+3}{2}<math>. It can also solve equations with complex solutions or variables.
The TI-89 also handles most calculus problems. It takes symbolic derivitives of all elementary functions and derivatives of some more complex functions too. the derivative function is d, and it takes two arguments, the function and the variable. It also takes an optional argument specifying what derivative to take (for example, making the optional argument 3 will take the third derivative). Entering in d((x^x-x)/(x-1),x) gives <math>\frac{(x-1)ln(x)+x-2)x^x+1}{(x-1)^2}<math>. When an exact solution can't be found or an approximate solution is desired, nDeriv can be used.
The calculator takes all existing integrals of elementary functions, and some of more complex functions as well. For example, ∫((x^2+1)^(-3/2),x) gives <math>\frac{x}{\sqrt{x^2+1}}<math>. By default, it doesn't add a constant of integration, but by assigning the integral a third parameter, it will use that as a constant of integration. By giving it a fouth assignment as well, it will evaluate the definite integral from the fouth parameter to the third. ∫((x^2+1)^(-3/2),x,1,y) gives <math>\frac{y}{\sqrt{y^2+1}}-\frac{\sqrt{2}}{2}<math>. In cases where no exact definite integral exists, it will approximate it. nInt will also approximate integrals.
The TI-89 can also take limits of functions. limit((1+1/x)^x,x,∞) is equivilent to <math>\lim_{x \to \infty}((1+1/x)^x)<math> and returns <math>e<math>.
In addition to the standard two-dimensional function plots, it can also produce parametric plots, polar functions, sequence plots, differential equation fields, and three-dimensional graphs.
Programming
The TI-89 is directly programmable in a language called TI-BASIC, TI's derivative of BASIC for calculator applications. Using a PC, one can also develop one's own programs in Motorola 68000 assembly language or C, translate them to machine language, and copy them to the calculator. Two software development kits for C programming are available; one is TI Flash Studio, the official TI SDK, and the other is TIGCC, a third-party SDK based on GCC.
Since 1998, thousands of programs for math, electronics, biology, or entertainment have been developed. Many available games are generic clones of Tetris, Minesweeper, and other classic games, but some programs are more advanced — for example, a ZX Spectrum emulator and a chess playing program.
Hardware Versions
There are two hardware versions of the original TI-89. These verions are normally referred to as HW1 and HW2. To find out which hardware version a calculator is, you should enter the key sequence [F1] [A]. If the dialog box displays "Hardware Version 2.00" then the calculator version is HW2. If the dialog box does not display any hardware information, the calculator is HW1. Unfortunately, the differences in the hardware versions are not well documented by Texas Instruments.
The most significant difference between HW1 and HW2 is in the way the calculator handles the display. In HW1 calculators there is a video buffer that stores all of the information that should be displayed on the screen, and every time the screen is refreshed the calculator accesses this buffer and flushes it to the display. HW2 calculators make changes to the screen dynamically, which means that the calculator's display hardware keeps track of changes that are made to the screen and then updates only those parts of the screen that have been changed. HW1 calculator displays, however, read the display memory again every time the screen is refreshed. This allows for a simple software implementation of grayscale that is unfortunately not compatible with HW2. Games written before HW2 was released thus display in black-and-white on HW2 calculators.
HW2 calculators are slightly faster because TI increased the nominal speed of the processor from 10 MHz to 12 MHz.
Another difference between HW1 and HW2 calculators is memory limitations. Unlike HW2 calculators, HW1 calculators have no memory limitations. The memory limitations that have been imposed on HW2 calculators has varied with the AMS version of the calculator. As of AMS 2.09 the memory limitation is 24k. There are, however, unofficial patches and kernels that can be installed on HW2 calculators to overcome these memory limitations.
TI-89 Titanium
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The TI-89 Titanium was released in the summer of 2004, and is positioned as a replacement for the popular (but now low-margin) TI-89.
The touted advantages of the TI-89 Titanium over the TI-89 are having roughly four times the available flash memory (with over three times as much available to the user). The TI-89 Titanium is essentially a Voyage 200 without an integrated keyboard, but with a mini-USB port for connectivity to other (TI-89 Titanium) calculators or to computers to add programs or update the operating system (also called the AMS - Advanced Mathematics Software). The TI-89 Titanium also features some pre-loaded applications, such as "CellSheet", a spreadsheet program also offered with other TI calculators. The Titanium also has a case design different from that of the TI-89.
There are some minor compatibility issues with C and assembly programs developed for the original TI-89. Some have to be recompiled to work on the Titanium due to various small hardware changes, though in most cases you can fix the problem on calc by using a utility such as GhostBuster, by Olivier Armand and Kevin Kofler (http://www.tigen.org/kevin.kofler/). This option is usually the best as it requires no knowledge of the program, works without the need of the program's source code, is automated, and doesn't require additional computer software. In some cases, only one character needs to be changed (the TI-89's ROM base is at 0x200000, whereas the TI-89 Titanium's is at 0x800000) by hand or by patcher. Most, if not all of these problems are caused by the Ghost Space, or lack of.
External links
- The largest collection of programs and other resources is ticalc.org (http://www.ticalc.org).
- A site with frequent news features, tutorials, active forums, a large and convenient archive and more is CalcGames.org (http://www.calcgames.org)
- A large collection of TI community news, polls, discussions, and reviews is available at ti-news.net (http://www.ti-news.net)
- For technical information on the TI-89, including a discussion of HW1,HW2, and HW3, visit [1] (http://www.ocf.berkeley.edu/~pad/faq/ti89.html)
- The aforementioned chess program and many programming utilities are available at the TI Chess Team website (http://tict.ticalc.org/).
- More sites can be found at the Open Directory Project TI-89 category (http://www.dmoz.org/Computers/Hardware/Calculators/TI_Graphing_Calculators/TI-89/).
- More Information on the TI-89 Titanium can be found at Texas Instruments' site (http://education.ti.com/us/product/tech/89ti/features/features.html).
- UnitedTI (http://www.unitedti.org/) - The largest, friendliest, and most active TI programming community.