TI-89 Tutorial

March 21, 2003
Updated on April 16, 2006

The TI-89 is a great calculator, it's one of the best calculators right now (there's the HP-49G which is a good calculator too, the TI-92 Plus offer the same specifications as the TI-89 but offers Geometry possibilities with the Cabri Géomoètre and the Geometer's Sketchpad).

For the latest and most up-to-date tutorial download this tutorial in PDF format: PDFTI-89 Tutorial

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Top Solving equations & system of linear equations:

solve(2x+3y+5z=-1 and -3x+5y-2z=3 and 5x-7y+8z=-2,{x,y,z})
zeros({2x+3y+5z+1 ,-3x+5y-2z-3 ,5x-7y+8z+2},{x,y,z})

Solve system of equations

Top Derivation & Integration:

Suppose we want to compute the derivative of : x2+3x-5
The syntax is

degree can be omitted,it's 1 by default


Compute the partial derivative fx of f(x)=sin(x*y) +cos2(x+y)

Partial derivative


Compute the double integral of : [x2 y + y2 +sin(y)] dxdy (we integrate for x supposing y constant then we integrate for y supposing x constant)

Double integral

Let's say we want to calculate the value of the integral of x*cos(x) between 1 and 10:


Top Limits, sums & Taylor expansions

Suppose we want to compute the limit of x2 when x tend to infinity


The syntax is:

direction is both 1 and -1 and can be omitted
1: limit from right
2: limit from left

sum k2 for k between 1 and n


Top Polynomials

The syntax is


Let's say we want to expand (x + y)4

Expanding polynomials

The syntax is:


Let's factor the function x2-9


Let's put on the same denominator the function: (1/x2)+(1/(y2+1))

Common Denominateur

Top Number operations:

Let's factor the number 1050 for example:

Factoring a number


GCD & LCM of many numbers:
Let's find the GCD & LCM of 3 numbers:



Let's see if 997 is prime or not
Testing if a number is prme

Let's find : 64!


Top Differential Equations

Let's solve the following differential equation: x''+w2x=0

We must rename x to y

Differential equations
Note that the result is: @3 cos (w.x)+@4 sin(w.x)
@3 and @4 are constants

Top Sequence

Suppose we want to find the terms of the following sequence: Un+1=2*Un+2 with U0=2
We can use 2 methods : the when function or by using the Sequence mode of the calculator.

1. when() function


2. Using the Sequence mode:

Let's take the previous example:
The syntax is:

ui1 is the initial term

sequence mode sequence mode table in the sequence mode
Note that the table start at 1 so en u0 is equal to n=1 on the calculator ,there is a shift of 1 between the calculator and the real world.