TI-89 series

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A TI-89

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. For many international math competitions, it is considered as the most powerful and function-rich graphing calculator that can be legally used (TI-92s and above have QWERTY keyboards).

1 The original version: TI-89
2 "Case-Swapping"
3 TI-89 Titanium
4 External links

[edit] 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. Many loyal 89 users refuse to make the switch to the TI-89 Titanium because of its new bubbly look.

The TI-89 runs on a 32-bit microprocessor called the Motorola 68000, 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.

[edit] User features

A screen capture of a 3D graph on the calculator

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 $x 2 - 4 x + 4$ . 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 $(x - 2) 2$ . The TI-89 can also expand factored expressions; entering expand((x-2)^2) yields $x 2 - 4 x + 4$ . 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

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

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

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

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

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

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

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

The calculator automatically reduces many trigonometric expressions; for example, sin(x)^2-1 equals $- (c o s (x)) 2$ . It even handles expressions such as sin(arctan(x^2-6)), returning

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

The tExpand function expands expressions such as sin(3x)cos(x) into $4sin(x)(cos(x)) 3 - sin(x)cos(x)$ . 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 $x = 3$ . 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

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

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

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

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

The TI-89 can solve simultaneous equations as well, with up to a 16 variables and 16 equations. To Solve

x - 2 y = 7

3 x + y = 5

Enter in simult([1,-2;3,1],[7;5]) Shows

$simult\begin{pmatrix} \begin{vmatrix} 1&-2 \\ 3&1 \end{vmatrix},\begin{vmatrix} 7 \\ 5 \end{vmatrix}\end{pmatrix}$

$\begin{vmatrix} 17/7 \\ -16/7 \end{vmatrix}$

With $17 / 7$ equaling x and $- 16 / 7$ equaling y respectively.

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 $d$ , 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

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

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

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

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

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

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

$\lim_{x \to \infty}((1+1/x)^x)$ and returns

e

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

[edit] 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.

.89u is the file type for the main operating system.

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. One of the most popular and well-known games is Phoenix. One person even re-created the popular game Link's Awakening.

[edit] Hardware versions

There are four hardware versions of the TI-89. These versions are normally referred to as HW1, HW2, HW3, and HW4 (released in May 2006). Entering the key sequence [F1] [A] outputs the hardware version in the form "Hardware Version ?.??". Older OS versions (before 2.00) don't display anything about the hardware version unless the calculator is HW2 or later. The differences in the hardware versions are not well documented by Texas Instruments. HW1 and HW2 calculators are in TI's classic calculator case; HW3 and HW4 are packaged in a new case design and sold under the name "TI-89 Titanium".

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). In HW2 and later calculators, a region of memory is directly aliased to the display controller (memory-mapped I/O). This allows for slightly 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 (a single write into a memory-mapped hardware register) and the screen will automatically use a new section of memory at the beginning of the next frame. In HW2, the new page must be written to the screen by 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. It is believed that TI increased the speed of HW4 calculators to 16 MHz, though many users disagree about this finding.

Another difference between HW1 and HW2 calculators is assembly program size limitations. The size limitation on HW2 calculators has varied with the AMS version of the calculator. As of AMS 2.09 the limit is 24k. Some earlier versions limited assembly programs to 8k, and the earliest AMS versions had no limit. HW1 calculators have no hardware to enforce the limits, so it is easy to bypass them in software. There are unofficial patches and kernels that can be installed on HW2 calculators to remove the limitations.

[edit] "Case-Swapping"

"Case Swapping" as it is commonly called is becoming increasingly common among TI-89 users. Users are taking the internal electronics of a TI-89 and putting them in another calculator’s shell, most commonly the TI-83+. This is most commonly done by students in an effort to evade school restrictions on advanced calculators with symbolic manipulation capabilities.[1]

Unscrupulous students have also been known to engage in "reverse case swapping", which involves removing the internal electronics of a TI-83 and placing them in a TI-89 case. The "TI-89" is then sold to an unsuspecting buyer for the typical price of a TI-89 model (usually about $30-50 more than the price of a TI-83). Potential buyers of used calculators can thwart reverse case swapping by simply switching on the calculator they are planning to buy and checking the hardware and operating system data on the About screen. On a TI-89, press HOME->F1->A to see this.

[edit] TI-89 Titanium

A 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. In 2006, new calculators were upgraded to HW4 which was supposed to offer increases in RAM and speeds up to 16MHz, but some benchmarks made by users reported speeds between 13-14MHz.

The touted advantages of the TI-89 include 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, except it doesn't have an integrated keyboard. The TI-89 Titanium also has a mini-USB port, for connectivity to other TI-89 Titanium calculators, or to a computer (to store programs or update the operating system). 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 slightly differing case design from that of the TI-89 (the Titanium's case design is similar to that of the TI-84 Plus)

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 the calculator 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.