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: TI-89 Tutorial

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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: -3x³ +3 x² -2x+5=0
The syntax is :
solve(-3x^3+3x^2-2x+5=0,x)
or
zeros(-3x^3+3x^2-2x+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:

2x-3y+5z=-1-3x+5y-2z=35x-7y+8z=-2

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

^Top Derivation & Integration:

Derivation

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

d(function,variable,degree)
degree can be omitted,it's 1 by default

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

Integration:
Let's say we want to integrate the function sin(x):

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)

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

Limits

Suppose we want to compute the limit of x² 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 k² 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 default
Suppose we want to know the 6th degree Taylor expansion of sin(x) around 0:

^Top Polynomials

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 x²-9

Common denominator:

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

^Top Number operations:

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:

Let's find : 64!

^Top Differential Equations

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

^Top Sequence

Suppose we want to find the terms of the following sequence: U_n+1=2*U_n+2 with U₀=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(n-1)+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(n-1)+2
ui1=2
ui1 is the initial term

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.

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