computer science

TI-89 series

TI-89 series is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand TI-89 series rather than just read about it. In short: The TI-89 and the TI-89 Titanium are graphing calculators developed by Texas Instruments (TI). They are differentiated from most other TI graphing calculators by their computer algebra system, which allows symbolic manipulation of algebraic expressions—equations can be solved in terms of variables— whereas the TI-83/84 series can only give a numeric result.

Key takeaways

TI-89 series belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect TI-89 series to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of TI-89 series from memory before moving on to harder problems.

Reference excerpt

The TI-89 and the TI-89 Titanium are graphing calculators developed by Texas Instruments (TI). They are differentiated from most other TI graphing calculators by their computer algebra system, which allows symbolic manipulation of algebraic expressions—equations can be solved in terms of variables— whereas the TI-83/84 series can only give a numeric result.

TI-89 The TI-89 is a graphing calculator developed by Texas Instruments in 1998. The unit features a 160×100 pixel resolution LCD and a large amount of flash memory, and includes TI's Advanced Mathematics Software. The TI-89 is one of the highest model lines in TI's calculator products, along with the TI-Nspire. In the summer of 2004, the standard TI-89 was replaced by the TI-89 Titanium. The TI-89 runs on a 32-bit microprocessor, the Motorola 68000, which nominally runs at 10 or 12 MHz, depending on the calculator's hardware version. The calculator has 256 kB of RAM, (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, text files, and lists. 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 not 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.

User features The major advantage of the TI-89 over other TI calculators is its built-in computer algebra system, or CAS. The calculator can evaluate and simplify algebraic expressions symbolically. For example, entering x^2-4x+4 returns x 2 − 4 x + 4 {\displaystyle x^{2}-4x+4} . The answer is "prettyprinted" by default; that is, displayed as it would be written by hand (e.g. the aforementioned x 2 − 4 x + 4 {\displaystyle x^{2}-4x+4} rather than x^2-4x+4). The TI-89's abilities include:

Algebraic factoring of expressions, including partial fraction decomposition. Algebraic simplification; for example, the CAS can combine multiple terms into one fraction by finding a common denominator. Evaluation of trigonometric expressions to exact values. For example, sin(60°) returns 3 2 {\displaystyle {\frac {\sqrt {3}}{2}}} instead of 0.86603. Solving equations for a certain variable. The CAS can solve for one variable in terms of others; it can also solve systems of equations. For equations such as quadratics where there are multiple solutions, it returns all of them. Equations with infinitely many solutions are solved by introducing arbitrary constants: solve(tan(x+2)=0,x) returns x=2.(90.@n1-1), with the @n1 representing any integer. Symbolic and numeric differentiation and integration. Derivatives and definite integrals are evaluated exactly when possible, and approximately otherwise. Calculate greatest common divisor (gcd) and least common multiple (lcm) Probability theory: factorial, combination, permutation, binomial distribution, normal distribution PrettyPrint (like equation editor and LaTeX) These mathematical constants are shown as symbols π {\displaystyle \pi } , e {\displaystyle e} , i {\displaystyle i} and ∞ {\displaystyle \infty }

Draw 2D and 3D graph Calculate taylorpolynomial Calculate limit of a function, including infinite limits and limits from one direction Vector calculation Matrix calculation Calculate series (summation or infinite product) Calculate chi squared test Calculate complex numbers Factoring polynomial: factor(polynomial) or cfactor(polynomial) Solve equation: solve(equation, x {\displaystyle x} ) or csolve(equation, x {\displaystyle x} ) Solve first or second order differential equation: deSolve(differential equation, x {\displaystyle x} , y {\displaystyle y} ) Multiply and divide SI Units: underscore _ "diamond" "MODE" A number of regressions: LinReg QuadReg CubicReg QuartReg ExpReg LnReg PowerReg Logistic SinReg 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 independent variable) functions.

Programming The TI-89 is directly programmable in a language called TI-BASIC 89, TI's derivative of BASIC for calculators. With the use of a PC, it is also possible to develop more complex 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. In addition, there is a third party flash application called GTC that allows the writing and compilation of C programs directly on the calculator. It is built on TIGCC, with some modifications. Numerous BASIC extensions are also present, the most notable of which is NewProg. Since the TI-89's release in 1998, thousands of programs for math, science, or entertainment have been developed. Many video games have also been developed. Many are generic clones of Tetris, Minesweeper, and other classic games, but some programs are more advanced: for example, a ZX Spectrum emulator, a chess-playing program, a symbolic circuit simulator, and a clone of Link's Awakening. Some of the most popular and well-known games are Phoenix, Drugwars, and Snake. Many calculator games and other useful programs can be found on TI-program sharing sites. Ticalc.org is a major one that offers thousands of calculator programs.

… excerpt ends here. Continue reading the full article.

Illustrations

TI-89 series: TI-89 shows table of y1 = ln(x) — TI-89 shows table of y1 = ln(x)

Worked examples

Example 1 — a first encounter with TI-89 series

Start with the simplest possible case. Write down what TI-89 series claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to TI-89 series before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about TI-89 series ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of TI-89 series

In research: TI-89 series appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses TI-89 series in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: TI-89 series is common in secondary-school and first-year university syllabi. It links to neighbouring topics 68k-based mobile devices, Computer-related introductions in 1998, Computer-related introductions in 2004, so understanding it makes those chapters shorter.
In everyday life: Look for TI-89 series outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study TI-89 series in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what TI-89 series means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain TI-89 series out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is TI-89 series in simple terms?

Why does TI-89 series matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study TI-89 series?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on TI-89 series.