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The TI-89 and the TI-89 Titanium are graphing calculators developed by Texas Instruments. The bulk of its users are students, who often find the built in Computer Algebra System invaluable. For this reason, the calculator is banned for use on the ACT and in some classrooms. It is, however, allowed by the College Board on all calculator-permitted tests, including the SAT, some SAT Subject Tests and the AP Calculus, Chemistry, Physics, and Statistics exams.

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 was dwarfed only by its larger and slightly more powerful cousin, the Voyage 200. In the summer of 2004, the standard TI-89 was replaced by the improved TI-89 Titanium.

The heart of the TI-89 is the Motorola 68000 microprocessor, which nominally runs at 10 MHz or 12 MHz (depending on the calculator's hardware version). 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, about the same size as most other graphing calculators. 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 ${\displaystyle x^{2}-4x+4}$. The answer is pretty printed by default; that is, it is returned as it would be written on paper, as opposed to how it would be entered into 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 ${\displaystyle (x-2)^{2}}$. The TI-89 can also expand factored expressions; entering expand((x-2)^2) yields ${\displaystyle x^{2}-4x+4}$. 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

${\displaystyle {\frac {5}{8(x+2)}}+{\frac {3}{8(x-6)}}}$.

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

${\displaystyle {\frac {12x+8y^{2}-3z^{2}-48}{24}}}$.

propFrac divides two expressions; an example would be propFrac((x^2-5)/(x-3)) returning

${\displaystyle {\frac {4}{x-3}}+x+3}$.

The calculator can evaluate trigonometric expressions to exact values. For example, sin(60°) returns

${\displaystyle {\frac {\sqrt {3}}{2}}}$.

The calculator automatically reduces many trigonometric expressions; for example, sin(x)^2-1 equals ${\displaystyle -(cos(x))^{2}}$. It even handles expressions such as sin(arctan(x^2-6)), returning

${\displaystyle (x^{2}-6){\sqrt {\frac {1}{x^{4}-12x^{2}+37}}}}$.

The tExpand function expands things such as sin(3x)cos(x) into ${\displaystyle 4\sin(x)(\cos(x))^{3}-\sin(x)\cos(x)}$. 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 ${\displaystyle x=3}$. 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

${\displaystyle x={\frac {\sqrt {2({\sqrt {13}}+1)}}{2}}\ {\textrm {or}}\ x={\frac {-{\sqrt {2({\sqrt {13}}+1)}}}{2}}}$.

For equations with infinite solutions, it solves them by introducing arbitrary constants. For example, solve(tan(x+2)=0,x) returns x=@n1${\displaystyle \pi }$-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

${\displaystyle x={\frac {{\sqrt {29}}+5}{2}}}$ and ${\displaystyle y={\frac {-({\sqrt {29}}-3)}{2}}}$ or ${\displaystyle x={\frac {-({\sqrt {29}}-5)}{2}}}$ and ${\displaystyle y={\frac {{\sqrt {29}}+3}{2}}}$.

It can also solve equations with complex solutions or variables with the function cSolve.

The TI-89 also handles most calculus problems. It takes symbolic derivatives of all elementary functions and derivatives of some more complex functions too. The derivative function is ${\displaystyle d}$, 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 ${\displaystyle d}$((x^x-x)/(x-1),x) gives

${\displaystyle {\frac {(x-1)\ln(x)+x-2)x^{x}+1}{(x-1)^{2}}}}$.

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

${\displaystyle {\frac {x}{\sqrt {x^{2}+1}}}}$.

By default, it doesn't add a constant of integration, but by providing the integral a third parameter, it will use that as a constant of integration. By giving it a fourth argument as well, it will evaluate the definite integral from the third parameter to the fourth. ∫((x^2+1)^(-3/2),x,1,y) gives

${\displaystyle \int _{1}^{y}(x^{2}+1)^{-3/2}\,dx={\frac {y}{\sqrt {y^{2}+1}}}-{\frac {\sqrt {2}}{2}}}$.

In cases where no exact definite integral exists, or when the calculator cannot find it, 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 equivalent to

${\displaystyle \lim _{x\to \infty }((1+1/x)^{x})}$ and returns ${\displaystyle e}$.

In addition to the standard two-dimensional function plots, it can also produce graphs of parametric equations, polar functions, sequence plots, differential equation fields, and three-dimensional (two variable) functions.

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, science, 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 versions are normally referred to as HW1 and HW2. Entering the key sequence outputs the hardware version. If the dialog box displays "Hardware Version 2.00" then the calculator version is HW2 and if it displays "Hardware Version 1.00", the calculator is HW1 (only newer OS' display "Hardware Version 1.00", older OS' don't display anything about the hardware version if your calc is a HW1 machine). 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 (direct memory access). On the HW2, a region of memory is directly aliased to the display controller (memory-mapped I/O). This allows for faster memory access, as the HW1's DMA controller used about 10% of the bus bandwidth; however, it interferes with a trick some programs use to implement grayscale graphics by rapidly switching between two or more displays (page-flipping). On the HW1, the DMA controller's base address can be changed and the screen will automatically use a new section of memory; on the HW2, the new page must be written to the screen in software. The effect of this is to cause increased flickering in grayscale mode, enough to make the 7-level grayscale supported on the HW1 unusable (although 4-level grayscale works on both 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 assembly program size limitations. Unlike HW2 calculators, HW1 calculators have no such limits. 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 limit is 24k. There are, however, unofficial patches and kernels that can be installed on HW2 calculators to overcome them.

In May 2006, Texas Instruments released hardware version 4 for the TI-89 Titanium. The speed of the processor is found to be estimated around 16 MHz. Many users disagree about this speed, however. The correct speed has not been determined yet.

"Case-Swapping"

"Case Swapping" is becoming increasingly common among TI-89 users as teachers are becoming aware of the calculator's capibilities and banning it from classroom use. Innovative users are taking the internal electronics of a TI-89 and putting them in another calculator’s shell, most commonly the Ti-83+.

TI-89 Titanium

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 TI-89 Titanium is referred to as HW3 and uses the corresponding AMS 3.x, 3.10 being the latest version.

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. 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 thereof.

External links

• Official website
• CalcGames.org - A site with frequent news features, tutorials, and forums
• Calchaven - Beginner-focused forum
• Cemetech - The largest archives of programs by a single author, plus a large community forum.
• JCP TI89 - Games, science, and math programs for the TI-89.
• The MF TI Calc Page - Fan site devoted to TI-89, TI-92, and TI-92 Plus graphing calculators
• Techno-Plaza - A good programming resource.
• ticalc.org - The largest collection of programs and other resources.
• TICALCS2 - Calculator downloads, news, forums, tutorials, and more.
• TI Chess Team - TI-Chess, TIGCC, and many other programming utilities.
• ti-news.net - A large collection of TI community news, polls, discussions, and reviews.
• Ultimate TI Calculator FAQ - For technical information on the TI-89, including a discussion of HW1,HW2, and HW3.
• Unitedti - Large community forum

• Graphing calculators