Brief Users Guide for the TI-89 Titanium
I. Basic Information - What's my operating
system version?, how much RAM do my programs
take, is my calc upgradeable?, adjusting brightness of display,
friendly values using TRACE,
navigating the APPS features, how to change settings, and how to obtain certain
symbols, what to do if
you have problems (see section XII of this document.)
II. Basic Math – Math operations, square roots, cube
roots and others, fractions
III. Special Expressions – Absolute Value, Greatest Integer,
etc. Finding primes of a number
IV. Graphing and Evaluating Functions – Graphing, finding zeros,
finding intersections of graphs,
graphing inequalities, marking points on a graph, etc.
V. Special Functions – Greatest Integer, Absolute Value,
Piecewise Functions, Trig Functions,
etc. Using [TABLE] to find points for graphing a parabola by hand.
VI. Polynomials - Expand an expression, Simplifying an
expression, Solving a polynomial, Solving an inequality,
Simplifying and expression, Solving polynomials with degree
higher than 2, graphing polynomials from the
polynomial application,
VII. Calculus – Finding the derivative of a function, finding the
implicit derivative, finding the numerical derivative
of a function, determining the value of the derivative at a
point on a graph, drawing a tangent line to a graph,
finding the anti-derivative of a function, finding the integral
of a function, implicit derivative, finding the limit.
VIII. Matrices – Determinant, Transpose, Row Operations, system of
equations
IX. Differential Equations - Draw slope fields, Draw slope
fields and solution, Draw solution without slope fields,
general and particular solution of an ODE, general and particular
solution of a second order diff. eq.
X. Sequences - Finding several terms of a sequence, finding a
specific term of a sequence,
summing sequences, cumulative sum of sequence, graphing a
sequence.
XI. Complex Numbers - Solving a polynomial with complex
coefficients,
XII. Transferring Programs and Data – Transferring data or
programs from one calculator to
another.
XIII. Problems:
RELEASE DATE: 8/28/07
DATE LAST REVISED: 7/28/08
Printer friendly page
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NOTE: Printing hints and copying limits are at the end of this document.
GENERAL: All keys have at least two functions and some have three. The default function for a key is the white print on the key. When 2nd is pressed the key function is as indicated in blue print on the panel immediately above the key. When the ♦ key (the yellow key with the diamond shape on it.) is pressed the functions in yellow print and activated. When ALPHA is pressed, the function is the white label immediately above the key and, in most cases, near the right end of the key. When APPS is pressed, the applications screen will appear if it is turned on in the MODE screen..
I. BASIC
INFORMATION
1) Turning the calculator ON and OFF.
a) To turn on: Press the ON key.
b) To turn off: Press 2nd; then OFF (the second function
for the ON key.) If an error message is displayed
you will need to press the Shift key (the diamond symbol) and then
press OFF.
2) Adjusting the contrast of the screen.
a) To make the screen display darker: Hold down the ♦ key (the key
below 2ND) and tap the + key.
b) To make the screen display lighter: Hold down the ♦ key and tap the
- key.
3) Finding your operating system version number.
a) From the APPS screen, press F1, 3. As of 6/21/07, the TI Website
listed the latest version of the OS as
Ver 3.10, 7-18-05.
4) Finding our how much free RAM I have.
a) Press 2nd; then MEM.
5) Is my calculator upgradeable? Yes, the operating system is upgradable and applications may be added.
6)
Friendly Values on Graphs Using TRACE:
Many times
when you use the TRACE function, you will get an x-value such as 2.784532. If
you change the x-min
and x-max in the WINDOW function to be multiples of 7.9 and the y-min and
y-max to multiples of 3.8 , the displayed
values will be "friendlier." That is, they will be integers or numbers
with one or two decimal places. You can always
set the values by hand, but the easiest method is to use the ZDecimal function
of ZOOM. Just press ZOOM; then
4, for ZDecimal.
It may be that the display is now partially off the screen. If you
want the entire graph on the screen, use the Zoom Out
function. To do that when in the graph mode, press F2; then 3, ENTER.
If you’re trying to find the value at a specific point, a zero for
example, and the cursor still does not fall on the x-axis,
you could try different strategies such as ZBox, but I usually prefer to
use the zero function. To do that, press F5, 2.
That will set you up for finding a root. Remember that any time you want
to get back to the standard window just
press F2, 6.
7. Using the APPS screen:
a) Press APPS to go to the screen that has icons for all of the
applications.
b) If the applications are not on the first screen, press the first
letter of the title of the icon you want to
select. For example, if you want to select Matrices D, the first
letter of the title Data/Matrices. For Lists
you would press S for statistics.
c) Press 2ND, APPS to toggle back and forth between the present screen
and the previous APPS screen. Note
that not all non-APPS screens are recalled by this method.
d) Another way to organize the APPS functions is to place them in
folders. As for myself, I have placed the
six APPS that I use most often in the MATH folder. That way when
I press APPS, I can then press
F1,2, 4 and my most-often-used APPS will immediately be displayed
on the screen. To organize the APPS, do
this:
1) Press APPS, F1, right cursor arrow, 3. A dialog box with a
list of APPS will appear on the screen. Scroll
up or down the list with the cursor arrows and press the
cursor right arrow to select one of the APPS.
8. Clearing the Calculator Screen.
a) To clear the calculator home screen: Press the F1, 8.
b) You can also use CLEAR to clear individual entries on the home
screen.
9. To move to another screen:
a) Press 2nd, QUIT to go to the APPS screen from any
screen.
10. Correcting errors or changing characters.
a) To replace a character at the cursor position, just press the new
character.
b) To insert a character in the position of the cursor, press 2nd,
press
INS, and then press the key for the desired character. Note that
you will need to press 2ND, INS
again to get out of the insert move and return to the strikeover
mode.
c) To delete a character to the right of the cursor, pulse ♦, DEL. You
can also use the backspace key (←) to delete
characters to the left of the cursor.
11. Changing the MODE:
(Use the MODE for such things as changing from degrees to radians,
displaying numbers as
powers of ten, using split screen, enabling complex number calculations,
turning off the APPS screen, changing the
language, and other similar things.)
a) Press the MODE key.
b) Use the arrow keys to move the cursor to the desired item.
c) Press the right cursor arrow to bring up a menu; then press the
number opposite the desired item on
the menu..
d) Press ESC to return to the last screen or 2ND, QUIT to return to the
APPS screen.
12. Performing numerical calculations:
a) On the graphing calculator screen, the multiplication symbol will
appear
as * and the division symbol will appear as /.
b) Parentheses can be used to denote multiplication or as grouping symbols
to
clarify the order of operations.
c) To enter an exponent use the ^ key for any exponent. Other functions
are available by pressing, 2ND,
MATH; then press the right cursor arrow and finally the number of the
item on the pop-up menu that
you desire.
d) Use the (-) key for negative numbers and the - key for subtraction.
II.
BASIC MATH
1. Raising a number to a power:
a) From the home screen, enter the number.
b) Press the ^ key
c) Enter the number for the power.
d) Press ENTER.
2. Finding the root of a number:
a) For square root, press 2nd; then the square root symbol (multiply
key).
b) Enter the number you want the square root of and close the
parentheses..
c) Press ENTER.
d) As an alternate method for the square root and for any other root, do
the following from the HOME screen:
1) Press, ♦, 9. The expression "root(" will be pasted to the
screen.
2) Enter the number and root according to the syntax root (number,
root). For example, the cube root of
27 would be root(27,3). Be sure to close the parentheses.
3) Press ENTER and the answer will be displayed. .
NOTE: For those who have used other TI calculators that
are very forgiving about omitting closing
parentheses, be aware that parentheses must be closed on the
TI-89.
3. Operations with fractions:
a) Use the divide symbol between the numerator and denominator. Ex: ¼
is
entered as 1÷4.
b) Use the correct operator symbol (divide, multiply, add, subtract)
between
fractions.
c) Note: How to set the Exact/Approx mode is a matter of
preference for numerical calculations. If you put it
in Exact, you will get no decimals, and if you put it in
Approximate, multiplying two fractions will give
a decimal. So, I usually leave it in Auto. In that mode, if you
want a decimal answer, you must add
a decimal to one of the numbers. For example, 5/2 would become
5.0/2.
4. Logarithms:
a. To find the common log, press ♦; then 7.
b. Enter the number, press ), and then press ENTER.
c. The natural logarithm is on the keyboard. Just press 2ND, the X-key;
close the parentheses and press ENTER.
III. SPECIAL EXPRESSIONS:
1. To enter the symbols, equal to, not equal to, greater-than, less
than, greater than or equal to, and less than or
equal to:
a) Press the 2nd ; MATH, 8.
b) Enter the item number for the desired symbol.
2. To find the absolute value of a number:
a) Press 2ND, MATH, 1, 2.
b) Abs( will be pasted to the home screen.
c) Enter your number, close the parentheses.
d) Press ENTER.
3. Finding the greatest integer function of a number.
a) From the Home screen, press the CATALOG key; then press the letter
I.
b) Move the cursor down to int( and press ENTER.
c) The expression int( will be pasted to the Home screen.
d) Enter your number and close the parentheses.
e) Press ENTER. (Note that this also works for negative numbers.)
4.
Finding the primes of a number.
a. From the home screen press F2,
2, and factor( will be pasted to the screen.
b. Enter the number you choose, close the parentheses, and press ENTER
to display the results.
IV. GRAPHING &
EVALUATING FUNCTIONS:
1. Graphing a function.
a) Press ♦, F1 to display the "Y=" screen. All equations must be in the
slope-intercept form, y=mx+b,
before entry. Note that only F1 and F2 are activated in this mode.
b) Enter the function(s) using the appropriate keys to enter the
variable.
c) Press ♦, GRAPH to graph the function. (If you don’t see your graph,
press
TRACE and use the arrows to find the maximum or minimum value of
your
function. Press ENTER and the graph should appear.)
d) To leave the screen without graphing, press Home.
e) Press CLEAR while the cursor is on the same line as the function to
erase the
function.
2. To obtain the standard size viewing window:
a) Press the F2 to go to the Zoom menu.
b) Press 6 to execute Z Standard.
3. To change the viewing window to a custom size:
a) Press ♦, WINDOW.
b) Use the cursor keys to move the to the value to be changed.
c) Enter the new value.
d) Press ♦, Graph to see the new graph, or press ♦, F1 to return to
the Y= screen.
e) ZSquare keeps the y-scale the same and adjust the x-scale so that
one unit on the x-axis equals one
unit on the y-axis.
f) ZDecimal makes each movement of the cursor equivalent to
one-tenth of a
unit.
g) ZInteger makes each movement of the cursor equivalent to one
unit.
4. Evaluating a function.
a) Press ♦, F1 and enter a function, y1 for example.
b) Press ENTER.
c) At the Home screen, enter y1(value) or for a series of values
y1({value, value, value}). For
example, y1({1, 2, 3})
d) Press ENTER and the values will be displayed.
5. To change or erase a function:
a) Press ♦, F1.
b) Use the arrow keys to move the cursor to the desired location and
make
changes by inserting, deleting, or changing the desired characters.
c) To erase a function, with the cursor on the same line as the
function, press the
CLEAR key.
6. To use the trace function:
a) From the Graph screen, press F3.
b) Use the right and left arrow keys to move the cursor along the
graph. The
coordinates of the cursor location are shown at the bottom of the
screen.
c) If more than one graph is on the screen, you can press the up or
down arrows
to jump from one graph to another.
d) To end the trace operation, press ESC.
7. Finding the maximum and minimum points.
a) Enter the function and graph it.
b) Press the F5. Press 3 for minimum or 4 for maximum.
c) Move the cursor to the left of the point where a minimum or maximum
appears to be and press ENTER.
d) Move the cursor to the right of the point and press ENTER.
e) The coordinates of the maximum or minimum will appear at the bottom
of the screen.
f) Press ESC to end this operation.
8. Finding the value of a function at a given value of x.
a) Enter the function and the graph it .
b) Press F5.
c) Press 1 to select value.
d) Enter the x-value and press ENTER. The x- and y-values will appear
at the bottom of the screen.
Press ESC to terminate this operation.
9. To zoom in using a box.
a) Enter the function and graph it.
b) Press the F2.
c) Press 1 to select ZBox.
d) Move the cursor above and to the left of the location you want
enlarged and
press ENTER.
e) Move the cursor below and to the right of the location you want
enlarged and
press ENTER.
f) The box is then enlarged to fill the screen. Press F2, 6 to return
to the Standard screen.
10. Finding the intersection point of two graphs.
a) Enter two functions on separate "Y=" lines and press ♦, GRAPH to
graph the equations. Equations must
be in slope-intercept form.
b) Press F5 to select the list of operations
c) Press 5 to select intersection. The cursor will appear on one of
the curves. Move the cursor
to a position so that the curves are clearly separated and to the
left of the first intersection point.
press ENTER. Press ENTER again if the cursor is on the second
graph; then press ENTER again
if the cursor is to the left of the intersection point.
d) The calculator will request the Upper Bound. Move the cursor to
the right of the first intersection
point but to the left of the second intersection point if there is
more than one intersection point.
e) Press ENTER and the coordinates for that particular intersection
point will appear at the bottom
of the screen. Press ESC to get out of this procedure.
f) If there is more than one intersection point, evaluate the other
points in the same way, except the
cursor will initially be placed to the left of the point you are
evaluating.
11. Solving an equation in one variable. (Also known as finding the
roots or x-axis intercepts.)
a) Enter the function and graph.
b) Press F5, 2..
c) Move the cursor to the left of the first x-axis intercept and press
ENTER.
d) Move the cursor to the right of that intercept and press ENTER.
f) The coordinates for the root (zero) will appear at the bottom of
the screen.
g) Additional zeros can be found by repeating this method for other
x-axis intercepts.
12. Finding
coordinates to graph a parabola by hand.
a) Enter the graph in your calculator as described above.
b) Next locate the vertex by pressing F5, and pressing either 3 or 4,
depending on
whether the vertex is a minimum or maximum for the parabola.
c) Move the cursor slightly to the left of the vertex and press
[ENTER].
d) Move the cursor slightly to the right of the vertex and press
[ENTER]. The x- and y-values
for the vertex will appear at the bottom of the screen
e) To find additional poinst, press [♦],[TABLE] and a table of (x,y)
values will appear. (You may want to set your independent
variable for Ask so that you can enter x-values of your own
choosing. If it is not set for Ask, press
[♦], [TBLSET] and press the right arrow key and press 2 for
"Ask," and a table will appear if you started the change from the
table screen .
f) Enter two more values for "x" in the table and the corresponding
values for "y" will appear.
g) Use these coordinates and the symmetry property of a parabola to
graph the parabola on a
sheet of paper. (NOTE: If the vertex is at an integer value,
you can find the vertex from the
table rather than using steps a through d to find the vertex.)
13. Graphing
Inequalities.
a) Write each equation in the y =mx + b format and enter them into
the "Y=" positions.
(Remember that you may need to change the direction of the
inequality sign if you have to
multiply by -1 during the rearranging of the equation.)
b) Select the graph to be shaded and press 2ND, F1 (to select F6).
c) Press 7 (Above) or 8 (Below) as appropriate and press ENTER.
The shaded graph will appear.
d) Press ♦, GRAPH and the shaded graph will appear.
14. Marking points
on a graph.
A few students who capture screens like to have marks on graphs.
Although some would
consider this more trouble than it's worth, I'll include it for those
brave souls who feel they must
have them.
a) First, if you are a little picky about having the marks line up
exactly on the graph, you
should press F2, 4 to select ZoomDec. Then graph your function
and see if the x-
and y-values that you are interested in appear on the screen.
If not, press F2 (Zoom), ALPHA, C to
select Set Factors. A dialog box will appear for setting xfact
and yfact. Make the xFact and yFact
integers larger than 1. Press ENTER to save the new zoom
factors.
b) Go to the Home screen to start the procedure. The syntax is
PtOff x,y. So, press
CATALOG, p, and cursor to PtOff.
c) Press ENTER and PtOff will appear on the Home screen.
d) Enter the x-coordinate, y-coordinate, and press ENTER. A barely
visible, for me, clear spot
will appear on the graph at the coordinates you selected.
e) To erase all points, press 2ND, F1,1, ENTER.
V. SPECIAL FUNCTIONS
1. Changing from radian measure to the degree mode:
a) Press the MODE key
b) Move the cursor to Angle and press the right cursor arrow to select
what you want.
c) Press ENTER to return to the previous screen.
2. Graphing piecewise functions or functions on an interval:
The piecewise expression has the form f1 if condition, else
f2. Let's graph this:
| x for x> 0
f(x) = | -x for x <0
a) Press ♦, F1 to display the Y= screen.
b) Enter "when" as as follows: Press CATALOG, w, select "when(" and
press ENTER.
c) Press x; then 2ND, MATH, 8 (for Test), 4 to enter <.
d) Press 0, [,], x, [,], (-), x). You should have "when(x< 0,
x, -x)" on the in the entry bar.
e) Press ♦, F3 (GRAPH) and the graph will be displayed.
VI. POLYNOMIALS
1. Expanding an Expression (can also be used for partial fractions):
a) From the home screen, press F2, 3. The expression expand(
will be pasted to the home screen.
b) Enter the number you want to expand, for example (x²-1)/(x^3 +2x²),
and close the parentheses. Your expression
should look like this: expand((x^2-2)/(x^3+2x^2))
c) Press ENTER and the answer will be displayed on the Home screen.
2. Simplifying
Algebraic Expressions:
1. Press F2, 7 to select propFrac(.
2. Enter your expression being careful to get the parentheses correct.
Example: profFrac((x^2 +3x +2)/(x+1)).
3. Press ENTER and the result will be displayed.
3. Factor a
Polynomial:
a) Press F2, to select factor(.
b) Enter your expression being sure to get the parentheses correct.
Example: factor(x^2 +5x +6).
c) Press ENTER and the result will be displayed.
4. Solving a
Quadratic Equation:
a) Press F2, 1 to select solve(.
b) Enter your equation. Example: solve(x^2+2x +3=11, x). Note that you
must have the variable, in this case x,
that you are finding the value for.
c) Press ENTER and the answer will be displayed.
5. Solving
Inequalities:
a) Press F2, 1 to select solve(.
b) Enter you equation and close the parentheses. Example: solve(x^2 +2>3,
x). The > symbol is obtained
by pressing 2ND, and the key below 2.
c) Press ENTER and the result will be displayed.
6. Solving
polynomials including those with degree higher than 2:
a) Press MODE, cursor to Complex Format and press the right cursor
arrow; then press 2 to select
rectangular unless you specifically want polar.
b) Press ENTER, APPS, select the Polynomial icon and press ENTER.
c) Press 3 for New. On the next screen, enter the degree of the
polynomial you are solving, for example 3, and
press ENTER.
d) Enter the coefficients for the terms starting with the highest degree
term. Press ENTER after each entry.
e) Press F5 and the solution will be displayed. To enter a new
polynomial, press ESC.
7. Graphing a
polynomial from the polynomial application:
a) Enter the polynomial coefficients according to the item directly
above.
1) Press F6 (that's 2ND, F1), 1, press the right arrow key.
2) Select Full for Split Screen, select y1 for Store Poly To, and
select whatever you want for ZOOM. If you
don't have a choice, start with ZoomStd.
3) Press ENTER and the graph will be displayed.
VII. CALCULUS
1. Finding the Derivative of an Function:
a) Press Home if not already at the Home Screen.
b) Press F3, 1 to select d( diferentiate.
c) Enter the function. For example, enter (x-y) 3/(x+y)
2 as follows:
d ( (, x, -, y, ), ^, 3, ÷, (,x, +, y, )^,2, comma, x)
so that d((x-y)^3/((x+y)^2, x) is displayed on the entry bar.
d) Press ENTER and the result will be given.
2. Finding the Implicit Derivative:
I believe that this is a new
capability that does not appear on the TI-89 (not Titanium), but, at the end of
this
discussion, I will suggest a method for finding the derivative implicitly
on the TI-89. Here is how to do it with
the TI-89 Titanium:
a) From the Home screen, press F-3, ALPHA, D, and impDif( will be
pasted to the
Home screen.
b) Enter information according to this syntax: impDif(x^2 + y^2 = 5,
x,y). Press ENTER and the implicit
derivative, -x/y, (1st derivative) will be displayed. If you
want the second, or even the third derivative, you
can add that after the dependent variable, y, as in the
following: impDif(x^2 + y^2 = 5, x,y,2). The 2 is for the
2nd derivative. For the first derivative, omit the number.
c) Press ENTER and the derivative will be displayed.
Now, how to do this with the TI-89 (not Titanium):
Remember some time back in the past you learned that if z is a
function of x and y, then you can write the
relationship below:
dy/dx = -(∂z/∂x)/(∂z/∂y) (Eq 1)
So, let's just take the derivative treating y as a constant; then the
derivative treating x as a constant.
Then we'll just plug them into Eq 1 above. We may need to do a little
simplification, but that should get
us close. Don't forget the negative sign in Eq. 1.
So, here are the steps to do x2 + y2 =5:
a) Press 2ND, MATH, ALPHA, 1 and d( will be pasted to the home screen.
b) Enter terms so that your entry looks like this: d(x^2+y^2 = 5,
x).
c) Press ENTER and the answer, -x, will be displayed. That's the
numerator.
d) Replace the "x" for the variable, the last x, with "y."
e) Press ENTER and -y will be displayed. That's the denominator.
g) Now, plug those into Eq 1 and you'll have dy/dx= -(-x/-y) = -x/y,
which is the same answer we obtained
with the TI-89 Titanium. Of course, you could define a variable,
but I'll leave that to the calculator geeks.
3. Finding the numerical derivative of a function:
a) From the Home screen, press the
F3, ALPHA, A. . The expression nDeriv( will be displayed
b) Enter the expression you want to find the derivative of. For
example, d(x^2)dx would be nDeriv(x^2,x).
c) Press ENTER and the result will be displayed.
4. Determining the value of the derivative from points on a graph:
a) First enter the function and graph it. The press the F5, 6,1. A
flashing cursor will be displayed on the graph.
b) Move the cursor to the point on the graph where you want to find
the derivative and press
ENTER.
c) The value of the derivative at that point will be displayed.
5. Drawing a tangent line at a point.
a) Enter the function and graph it.
b) From the graphing screen, press F5, ALPHA, A.
c) Move the flashing cursor that appears to the point where you want
the tangent and press ENTER.
d) The tangent line will be drawn at that point.
e) To clear the tangent line, press ESC, F4.
6. Finding the Antiderivative of a Function:
a) From the Home screen, press 2ND, ∫, (the number 7 key).
b) Enter the expression of interest. For example ∫ x^2 dx would be ∫
(x^2, x)
e) Press the ENTER and the antiderivative will be displayed.
7. Calculating the value of a definite integral:
a) Graph the function of interest and press F5, 7.
b) Move the flashing cursor to the lower limit you desire and press
ENTER; then move the
cursor to the upper limit you desire and press ENTER
c) The area will be shaded and the value of the are will be displayed.
8. Finding the
limit of a function:
a) From the Home screen, press F3, 3 to paste limit( to the screen.
b) The syntax is "limit( expression, var, point, direction)," where
direction from the left is -1 and from
right is 1. Lets do the limit of 1/x as x approaches 5.
c) Enter information so that you have "limit(1/x, x, 5).
d) Press ENTER and the answer, .2 will appear.
e) To find the limit of the same expression as x
→∞, erase 5 and press
♦, CATALOG to paste
∞ to the
screen.
f) Make sure the parentheses are closed; then press
ENTER and the answer, 0, will be displayed.
VIII. MATRICES:
General: When it comes to doing matrices, there are different ways of
setting them up and editing them,
but I am going to stick with one way. If you want to try another, read your
user manual (good luck.). I'm first
going to tell you how to set up a matrix using the Data/Matrix editor; then I'll
show you how to edit a matrix
that has already been set up. Finally, I will tell you how a teacher might set
up his calculator to save lecture
time with the details.
1) Entering and Editing a Matrix:
A) Entering a Matrix:
a) Press [APPS] if you're not already at the APPS menu; then
select the Data/Matrix icon and press
[ENTER]. Press 3 to select New. Note: When you go to the APPS
screen, the Data/Matrix icon
may not be displayed on the screen. To display a group which has
the Data/Matrix icon, press D.
b) With the cursor opposite Type, press the right cursor arrow and
press 2 for Matrix.
c) Move the cursor down to the space for Variable and type in whatever
variable you want. Type in whatever
unrestricted variable you choose. If you intend to retain this
matrix, I suggest you not use the
variables a-z because sometimes it is convenient to clear all of
these at the same time.
d) After you have entered the variable move down and enter the number
of rows and columns; then
press ENTER and the matrix table will be displayed.
e) You can now either enter data or press Home and edit the matrix
when you need it. To enter data, enter
each value and press ENTER. The cursor will automatically move to
the next position for the next entry.
f) After you are finished, press Home to go to the home screen.
B) Editing a Matrix:
a) Press [APPS] if you're not already at the APPS menu; then
select the Data/Matrix icon and press
[ENTER]. Press 2 to select Open
b) Press the right cursor arrow and press 2 to select Matrix; then
move the cursor down to Variable, press
the right arrow, select the matrix you want and press ENTER,
ENTER. The matrix will be displayed for
editing.
c) Enter data and press ENTER after each entry.
d) After you've entered all of the data, press Home to go to the
home screen for matrix operations.
Note: If you want to display a matrix from the home screen
you can Press 2ND, VAR-LINK (the minus key),
F2, cursor to Var Type, press right cursor, 4, ENTER. Then
highlight the matrix you want and press
ENTER. The matrix name will be displayed. Press ENTER and the
matrix will be displayed on the Home
Home screen.
C) Comments:
a) As I go through the operations you will notice that I have
variable names for my matrices that may seem
to you to waste memory. I have done that because I mostly
teach others how to do matrices, and my
method seems to save time for me. I have chosen to store
permanently matrices of several different
dimensions and to give them variable names so that I can
immediately identify what dimensions they
have. For example, Matrix m134 would be the first of the 3x4
matrices; m234 would be the second.
2) Multiplying two matrices [m133] * [m233]:
a) Enter the data into matrices [m133] and [m233] according to
"Editing a Matrix" above, and press Home
to go to the home screen.
b) From the home screen, enter the name of the matrix, e.g., m133.
c) Press x (the multiply sign) and enter the name of the second matrix, e.g.,
m233.
d) Press ENTER to perform the multiplication step.
e) Remember that the numbers of columns in [m133] must equal the
number of
rows in [m233] or you will get a dimension error.
3) Doing other matrix math:
a) Press 2nd, MATH, 4. On a pop-up list you will see a list of
operations that you can do. To find the
transpose, use T; to find the determinant, use det(, to find the reduced row-echelon form
use rref(, and
so on with the other operations. .
b) After you select the operation you want, press ENTER and the
operation will be pasted to the home screen..
c) Enter the variable name of the matrix you want and close the
parentheses.
d) Press ENTER again to get your answer.
NOTE: You can do any of the elementary row operations, swap rows,
multiply a row by a constant, add two rows,
multiply one row by a constant and add it to another row, by pressing 2ND, MATH,
4, ALPHA, J, pressing the right arrow
key and selecting the operation you want to do. They are very useful for doing
the arithmetic for Gauss or Gauss-Jordan
elimination, but
considerable time is required to get the hang of doing row operations. So, since
most students don’t take the time
to use those functions, I’m not going to include them. Instead, I’ll give you
my Website as a reference for doing those operations if
you want to do them. If there are enough request, I will include that.
4) Doing rref and ref:
Since rref and ref are used extensively in our college, I'm going to
include them as separate items.
a) First enter the data in your matrix (First set up the matrix if you
do not already have one set up.)
as outlined above and press Home to go to the home screen.
b) Press 2ND, MATH, 4; then 3 for ref( and 4 for rref(. The chosen
operation will be pasted to the
Home screen.
c) Enter the name of the matrix where you entered your data, e.g.,
m134, and close the parentheses.
d) Press ENTER and the new matrix will be displayed on the home
screen. Of course, to clear the screen,
press F1, 8.
5) Solving a system
of linear equations:
Let's take the following set of simple equations:
3x -3y = -2
2x +y = 1
Entering Data in the matrix:
a) Press [APPS] if you're not already at the APPS menu; then
select the Data/Matrix icon and press
[ENTER]. Press 2 to select Open. (Note: If you do not have a 2x2
matrix stored in your calculator,
follow "Entering a Matrix" above to set up your matrix.
b) On the dialog box that appears, press the right cursor arrow and
press 2 to select Matrix; then move the cursor down to
Variable, press the right arrow, select the matrix you want and
press ENTER, ENTER. The matrix will be displayed.
c) Enter each value of the matrix and press ENTER after each
value. Enter only the coefficients of the
variables and the constants. Do NOT enter variables, or plus
signs, but do enter negative signs (not minus
signs.). Enter the numbers 3, -3, -2, 2, 1, 1 and press ENTER
after each number.
d) When your are finished entering data, press Home to go to the
home screen.
Note: If you want to display a matrix from the home
screen you can Press 2ND, VVAR-LINK (the minus key),
F2, cursor to Var Type, press right cursor, 4, ENTER. Then
highlight the matrix you want and press
ENTER. The matrix name will be displayed. Press ENTER to
display the matrix.
Solving the system of equations using the rref operation:
e) Press 2ND, MATH, 4; then press 4 for rref(. The chosen
operation will be pasted to the
Home screen.
f) Enter the name of the matrix where you entered your data, e.g.,
m134, and close the parentheses.
g) Press ENTER and the new matrix will be displayed on the home
screen. Of course, to clear the screen,
press F1, 8.
IX. DIFFERENTIAL
EQUATIONS:
1) Draw the slope field for a differential equation:
Let's take the very simple example y' = 2x .
a) Press MODE, press the right cursor arrow. Press 6, ENTER
to set up the Y= screen for differential equations.
b) Press ♦, F1 to display the y= screen.
c) Press ♦, | (the key above EE) to display GRAPH FORMATS dialog
box. The fields there
should be as follows: Axes = ON, Labels = ON, Solution Method
= RK, and Fields= SLPFLD .
d) Press ENTER to return to the Y= screen.
e) Enter 2t and press ENTER. Do not put a initial value for yi1
at this time.
f) Press ♦, F3 and the slope field will be drawn. Note that with
some equations, considerably
time may be required for a solution. "Busy" will appear on
the right bottom of the screen while the solution
is being arrived at.
2) Draw the slope field and graph for a differential equation:
a) Do the same as in item 1 immediately above, but opposite yi1
enter a constant such as -1.
b) Press ♦, F-3 and the slope field and the graph will be drawn.
3) Draw
graph for a differential equation without slope field:
Do the same as in item 1 immediately above except for the
following:
a) Opposite yi1 enter a constant such as -1.
b) During setup in step "c" in item 1 above, turn the slope
fields off by pressing the right arrow until
FLDOFF appears. If you have already done the equation with
a slope field and want to eliminate
it, press ♦, | (key above EE), cursor to Fields, press the
right cursor arrow, and press 3.
c) Press ENTER to return to the Y= screen.
d) Press ♦, F3 to graph the solution to the differential
equation. Note that if you don't have a value
entered in Yi1, the graph will not be drawn.
4) Find
the general and particular solutions to first order and ODE:
General solution of dy/dx = 2x.
a) From the Home screen, press F3, ALPHA, c to paste deSolve( to
the screen.
b) Enter information so that you have deSolve(y' =2x,x,y). The
prime symbol is obtained by pressing
2ND, = or by pressing 2ND, CHAR ( the + key), 3, 7.
c) Press ENTER and the answer will be given. Note that @1 would
be C1 in a calculus book.
Now, find the particular solution when y = 6 and x=2.
d) Press 2ND, ans (the minus key).
e) Press 2ND, MATH, 8,8 to past "and" to the screen.
g) Enter y(2) =6, so that you have "ans(1) and y(2)=6.
h) Press ENTER and the answer will be displayed.
Note that if you wanted that particular solution form the
beginning, you could have entered
deSolve(y'=2x and y(2)=6, x, y), and then pressed ENTER
5) Find
the general and particular solutions of a second order differential equation:
Solve y" +5y' -2y' -5y = 0
a) From the Home screen, press F3, ALPHA, C to paste deSolve( to
the Home screen.
b) Enter the equation so that the entry looks like the
following: deSolve(y" -2y' -5y=0, x,y).
Notice that the prime symbol is entered by pressing 2ND;
then the = key. For the
double prime, you will need to press 2ND, = for each of the
two primes.
c) Press ENTER and the solution will be displayed.
d) Solve for the particular solution as in the procedure above
except that you will add "and
y(2)' = 3 or some such value as required by the problem.
Important Note:
When you're finished with differential equations, don't forget to change the
mode back to
function with the strokes MODE, right cursor arrow, 1, ENTER.
X. SEQUENCES:
1) Find the first four terms of the sequence an =3n-2.
a) From the Home screen, press 2ND, MATH, 3, 1. The term seq(
will be pasted to the Home
screen.
b) Enter 3; ALPHA; n; -,2, ALPHA; n, 1,4, ). You now should have
seq(3n-2, n, 1,4) on the
home screen.
c) Press ENTER and {1 4 7 10} will be displayed.
2) Find
the sum of the sequence above.
This type problem will usually be written using the summation
symbol, Σ.
a) From the Home screen, press 2ND, MATH,3, 6 and sum( will be
pasted to the Home
screen.
b) Press 2ND, MATH, 3, 1 and seq( will be pasted to the screen.
You should now have sum(seq( on the Home
screen.
c) Enter 3; ALPHA; n; -,2,ALPHA; n, 1,4),) You now should have
sum(seq(3n-2, n, 1,4 ))
displayed on the home screen.
d) Press ENTER and 22 will be displayed.
3) Find
the cumulative sum of the above sequence.
a) From the Home screen, press 2ND, MATH,3, 7 and cumsum( will be
pasted to the Home
screen.
b) Press 2ND, MATH, 3, 1, ) and you should have: cumsum(seq( on
the home screen.
c) Enter 3; ALPHA; n; -, 2,ALPHA; n,1,4,),) and you should have
cumSum(seq(3n-2, n, 1,4))
on the Home Screen.
d) Press ENTER and {1 5 12 22} will be displayed. Note that
this method gives the sum after each
increment of the variable n.
4) Find the 5th term of the above sequence.
Although this is easily done by hand, some students like to check
their results. So here's how to
do it with your calculator.
a) Press 2ND, MATH, 3, 1, ENTER and seq( will be pasted to the
Home screen.
b) Enter 3; ALPHA; n; -,2,ALPHA; n, 5,5,). You now should have
seq(3n-2, n, 5,5) on the
home screen. (Note that the same number is entered for the
beginning and end.)
c) Press ENTER and {13} will be displayed.
5)
Graphing a sequence:
a) Press MODE, press the right cursor arrow and press 4 for
sequence. Press ENTER.
b) Press ♦, F1 and enter the sequence.
c) Enter the sequence, for example n^2-n and press ENTER;
then enter an initial value in ui1
if you want one and press ENTER.
d) Press ♦, F3 and the values will be plotted. You may want to
change the WINDOW to get
more values on the screen.
Don't forget to change the MODE back to Function when you're finished with
the sequences. To do
that, press MODE, right arrow, 1.
XI. Complex Numbers:
1. Solving a Polynomial with Complex Coefficients:
a) Press APPS, select the
Polynomial icon, and press ENTER.
b) On the screen that appears, enter the degree, for example 2 and
press ENTER.
c) On the screen that appears, press 3 for New.
d) Enter the complex coefficients and press F5. The complex
values for "x" will be displayed.
XI. TRANSFERRING PROGRAMS AND DATA:
1) I will assume that both calculators are TI-89:
a) Turn both calculators off and plug in
the unit-to-unit cable for both calculators.
b) Press 2ND, VAR- LINK on the sending unit to display the
VAR-LINK screen.
c) On the sending unit, highlight an item you want to send and
press F4 to check it.
d) On the receiving unit, press 2ND, VAR-LINK to display the
VAR-Link screen. .
e) On both units, press F3, Link to display menu options.
f) On the receiving unit select 2: Receive. On the sending unit
select 1: Send
g) If everything is connected satisfactorily, transmission of the
program should
start. Otherwise, you'll get a transmit error after a few
seconds.
XII. PROBLEMS:
These are instructions from the TI manual. I do not vouch for
their effectiveness.
1. If the BATT test is highlighted, replace
the batteries as soon as possbible.
2. The TI-89 Titanium does not appear to be
working properly.
a) Press ESC
several times to exit any menu or dialog box and to return the cursor to the
entry line.
Also, be sure the batteries are not exhausted.
3. The TI-89 Titanium appears to be locked up and
will not respond to keyboard input.
CAUTION: This procedure clears all RAM. It erases all data,
programs, and user-defined variables, functions,
or folders.
a) Press and hold
and hold down all at the same time these keys: Left arrow, right arrow,
and 2ND. Then
press and release ON.
CAUTION: This procedure clears all
RAM. It erases all data, programs, and user-defined variables, functions,
or folders in
addition to Flash applications, and the user data archive.
a) Remove one
of the four AAA batteries.
b. Press and
hold the minus, (-), and ) keys as you reinstall the battery.
c. Continue
holding (-) and ) for five seconds before releasing
6/20/07 - Problems
may be added later. If you have any you'd like to see listed, send them
to me.
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