Calculator Workshop

TI-83 and TI-89 Titanium

The calculator should not be

used as a crutch • If you do not know how to do a problem without your

calculator and you are expected to, then be careful using

your calculator. Your calculator can give you an answer, but

it does not show you how to get there.

TI-83

How to make good use a TI-83, TI-83+, TI-84 or TI-84+

Solver

• Access by going to “Math” then going to the bottom of the first menu

• Type in the right hand side of an equation where the left side is 0.

• Press down

• Type an initial guess

• Press Alpha, then enter

• This solver uses Newton’s method

Special Variables

• All Function, Parametric and Polar variables can be found

by pressing VARS then scrolling over to Y-VARS

• If Y1=2*X then “Y1(2)” gives “4”

Special Symbols: Inequalities

• Under TEST (2ND,MATH) you will find =,≠,>,≥,

Special Symbols: Angles

• Under “ANGLE” (2ND,APPS) there are degree and radian

symbols so that you do not have to go into mode if you

choose not to.

• There are also functions for converting complex numbers

here. Numbers must be entered as ordered pairs

Graph Tools

• Under “Calc” (2ND,TRACE)

• Value, zero, minimum, maximum, intersect, dy/dx,

∫f(x)dx

• Using the “TEST” symbols from the previous

slide we can define piecewise functions in

“Y=“

• Ex:

• “Y1 = X^2(X>0)” graphs the right half of y=x2

Different Modes and How to

Use Them • You can set the number of digits to round to,

the exponential format, the angle format, the

graph type, complex format and several graph

options

• “Connected” and “Dot” refer to how the graph

will be drawn

• “Sequential” and “Simul” tell the calculator

whether to graph functions in order or all at

once

Programming & TI-Basic

• Works like most programming languages

• Get to programming commands by pressing

“PRGM”

• Use “Prompt” to get values from user

• Use “Disp” to output values

• Ex:

• “Prompt a,b” will ask for a, then b and store both in

a and b

TI-89 Titanium

(Also the TI Voyage 200 if you happen to have one at

hand)

Solvers

• Solve(equation,variable) • Solves “equation” for “variable” in real numbers

• Csolve(equation,variable) • Solves “equation” for “variable” in complex

numbers

• Desolve(Diff eq,v1,v2) • Solves “Diff eq” for “v2” as a function of “v1”

• Use single quote to denote derivative (double for second derivative and so on)

• @1, @2… are constants like c1, c2…

Expand, Factor, Texpand,

Tcollect • Expand(expr)

• Expands the expression “expr”

• Factor(expr)

• Factors the expression “expr”

• Texpand(expr)

• Expands “expr” using some trig identities

• Tcollect(expr)

• Factors “expr” using some trig identities

Integrals, Derivatives, Sums

• ∫(f,v) integrates f(v)dv

• ∫(f,v,a,b) integrates f(v)dv from a to b

• d(f,v) takes derivative f’(v) in terms of v

• d(f,v,n) takes nth derivative f(n)(v)

• ∑(expr,v,a,b) sums “expr” where v goes from a to b

Limit and ∞

• Limit(expr,v,a) takes the limit of “expr” as v goes to a

• Ex:

• Calculating limit(1/x,x,0) gives ∞

• ∞ = infinity

• There is a button for this

Define

• Define f(x)=expr

• Makes f a function of x with value “expr”

• “expr” should be in terms of x

• Define f(x,y)=expr also works

• Ex:

• Define f(x)=x^2

• Calculating f(2) will give 4

Logical expressions

• And, or, not (~)

• The calculator knows what these are

• If you type an expression with them it will try to evaluate it

• Ex:

• “(a or b) and c” gives “a and c or b and c”

• “not ( true or false)” gives “false”

• “not a” gives “~a”

Conditional expressions (|)

• You can impose conditions on things with the “|” symbol

• Ex:

• “x^2+2 | x=7” gives “51”

• “(x+y)*z |x+y=2” gives “2z”

• “(x+y)*z|x=1 and y=1” gives “2z”

fMax, fMin

• fMax(expr,v) finds the maximum point of expr in terms of v

• fMin(expr,v) finds the minimum point of expr in terms of v

• Ex:

• “fMin(x^2,x)” gives “x=0”

Special variables

• All y, z, xt, yt, r, and u variables can be accessed by typing

them in.

• Ex:

• If y1=x^2 in the “Y=“ window “y1(3)” gives “9”

Mode (Graph)

• Function, Parametric, Polar, Sequence, 3D and Diff Equations are all options

• Function is default

• Sequence is for integer inputs

• 3D only graphs one function at a time, but you can rotate the graph

• Diff Equations graphs a slope field with the option of an initial value, but equations must be solved first.

More Modes

• “Display Digits” tells the calculator how many digits to display

• “Exponential Format” tells it what notation to use

• “Complex Format” tells it how to format complex numbers

• “Vector Format” tells it how to farmat vectors

Modes Continued

• “Split Screen” and the 5 options below it (4 are normally grayed out) lets you display multiple windows at once

• “Exact/Approx” tells the calculator whether to use decimals or not

• “Auto” tells it to use decimals if and only if there is a decimal in the computation

• Approximating can be forced by pressing the green button before hitting enter

Modes Concluded

• “Angle” lets you switch between radians and

degrees

• “Base” lets you use binary or hexadecimal

numbers

• You can input these numbers in other modes by

typing “0b” or “0h” before the numbers

• You can convert to these bases using the symbol

that looks like a right-pointing, filled-in triangle

followed by the desired base (bin, hex or dec)

Programming

• Programming is essentially the same as for the TI-83 with

only a few changes:

• You can now define functions that your calculator can use.

These cannot use things like loops and must be mathematical

expressions. “Disp” is not used.

• You can specify inputs to your programs and functions.

The Catalog

• For more useful functions, try browsing the catalog. It has

all of the functions that the calculator knows.

• This is true of all TI graphing calculators.