TI89 Tutorial
March 21, 2003
Updated on April 16, 2006
The TI89 is a great calculator, it's one of the best calculators right now (there's the HP49G which is a good calculator too, the TI92 Plus offer the same specifications as the TI89 but offers Geometry possibilities with the Cabri Géomoètre and the Geometer's Sketchpad).
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 Equations & system of equations
 Limits, sums & Taylor expansions
 Number operations
 Sequence
 Derivation & integration
 Polynomials
 Differential Equations
^{Top} Solving equations & system of linear equations:
 Suppose we want to solve the following equation:
3x^{3} +3 x^{2} 2x+5=0
The syntax is :solve(3x^3+3x^22x+5=0,x)
or
zeros(3x^3+3x^22x+5,x)I have written ",x" after the equation because the variable to solve for in this equation is x
 Suppose we want to solve the following system
of equations:
2x3y+5z=1
3x+5y2z=3
5x7y+8z=2
^{Top} Derivation & Integration:solve(2x+3y+5z=1 and 3x+5y2z=3 and 5x7y+8z=2,{x,y,z})
or
zeros({2x+3y+5z+1 ,3x+5y2z3 ,5x7y+8z+2},{x,y,z})
 Derivation
Suppose we want to compute the derivative of : x^{2}+3x5
The syntax isd(function,variable,degree)
degree can be omitted,it's 1 by default
Compute the partial derivative fx of f(x)=sin(x*y) +cos^{2}(x+y)
 Integration:
Let's say we want to integrate the function sin(x):
^{Top} Limits, sums & Taylor expansions
Compute the double integral of : [x^{2} y + y^{2} +sin(y)] dxdy (we integrate for x supposing y constant then we integrate for y supposing x constant)
Let's say we want to calculate the value of the integral of x*cos(x) between 1 and 10:
 Limits
Suppose we want to compute the limit of x^{2} when x tend to infinity
The syntax is:
lim(function,variable,point,direction)
direction is both 1 and 1 and can be omitted
1: limit from right
2: limit from left
 Sum:
sum k^{2} for k between 1 and n
 Taylor expansions:
The syntax for computing Taylor series is:
taylor(function,variable,degree,point)
point can be omitted , it's 0 by defaultSuppose we want to know the 6th degree Taylor expansion of sin(x) around 0:
 Expanding polynomials
The syntax is
expand(polynomial,variable)
Let's say we want to expand (x + y)^{4}
 Factoring polynomials
The syntax is:
factor(function,variable)
Let's factor the function x^{2}9
 Common denominator:
^{Top} Number operations:Let's put on the same denominator the function: (1/x^{2})+(1/(y^{2}+1))
 Factoring a number:
factor(number)
Let's factor the number 1050 for example:
 Finding the GCD (Great Commun Divisor) & LCM (Least Commun Multiple) of 2 numbers:
gcd(number1,number2)
lcm(number1,number2)GCD & LCM of many numbers:
Let's find the GCD & LCM of 3 numbers:gcd(gcd(number1,number2),number3)
lcm(lcm(number1,number2),number3)
 Testing if a number is prime or not
isPrime(number)
Let's see if 997 is prime or not
 Finding the factorial of a number:
^{Top} Differential EquationsLet's find : 64!
^{Top} SequenceLet's solve the following differential equation: x''+w^{2}x=0
deSolve(function,x,y)
We must rename x to y
Note that the result is: @3 cos (w.x)+@4 sin(w.x)
@3 and @4 are constants
Suppose we want to find the terms of the following
sequence: U_{n+1}=2*U_{n}+2 with
U_{0}=2
We can use 2 methods : the when function or by using
the Sequence mode of the calculator.
1. when() function

The syntax of this function is :
when(condition,true value,false value,unknown value)
false value & unknown value can be omitted.when(n=0,2,2*u(n1)+2) >u(n)
The sign " > " is to store the function in u(n)
To compute u, we write : u(1)
Suppose we want to find the 5 first terms of the sequence, we should write:
{u(1),u(2),u(3),u(4),u(5)}
 2. Using the Sequence mode:

Let's take the previous example:
The syntax is:
u1=2*u1(n1)+2
ui1=2
ui1 is the initial term
Note that the table start at 1 so en u_{0} is equal to n=1 on the calculator ,there is a shift of 1 between the calculator and the real world.