Texas Instruments Titanium TI-89 Manual

8/10/01 © 2001 Texas Instruments
TI-89 / TI-92 Plus
Calculus Tools
Getting Started
What is the Calculus Tools Application?
Before You Begin
Starting the Calculus Tools Application
Calculus Tools Menus
F1:Tools F4:Seq
F2:Deriv F5:Vector
F3:Integ F6:Advanced
More Information
Calculus Tools Application Functions
TI

TI-89 / TI-92 Plus Calculus Tools Page 2
Important Information
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Graphing product applications (Apps) are licensed. See the
terms of thelicense agreementfor this product.
TI-GRAPH LINK is a trademark of Texas Instruments.
All other trademarks are the property of their respective owners.

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What is the Calculus Tools Application?
The Calculus Tools application (App) is a Concept software
application for the TI-89 / TI-92 Plus. Concept software
applications are calculator software application prototypes that
demonstrate a new concept area.
The Calculus Tools App extends the built-in power of your
TI-89 / TI-92 Plus by providing more specialized functionality.
Use the Calculus Tools App to investigate applications of
differentiation; compare numerical integration techniques; and
explore sequences, series, vector calculus, Fourier series, and
more.
The Calculus Tools App is based on programs written or
evaluated by CAS (Computer Algebra System) experts and
educators Bernhard Kutzler, Bhuvanesh Bhatt, David R.
Stoutemyer, Josef Böhm, Ray Barton, Ruth Dover, and
Wolfgang Pröpper. We appreciate their contributions and
evaluations.
Additional documentation for many of the Calculus Tools App
features can be found at series.bk-teachware.com. Other
teaching and learning materials written for the TI-89 and
TI-92 Plus are also available at the Web site, including Exploring
Integration with the TI-89/92/92+ by Josef Böhm and Wolfgang
Pröpper.

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Before You Begin
Concept applications are shared with our customers, educators,
and students before product definition and testing is complete.
These applications may contain software imperfections and/or
incomplete coding areas. They are "alpha" software versions.
TI invites feedback from teachers and students concerning the
functionality and educational value of the Calculus Tools App.
Please send your comments and questions to
[email protected].
Mode settings
The Calculus Tools App requires specific mode settings to run
correctly. If you try to access the application with incorrect mode
settings, this error dialog box will appear:

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Before starting the Calculus Tools App, set modes to the
required values as follows:
1. From the Home screen, press 3to display the MODE
dialog box.
2. Ensure that the following modes are set as indicated:
Mode
Setting
Graph
FUNCTION
Display Digits
FLOAT or FLOAT # (1 -12)
Angle
RADIAN
Split Screen
FULL
Exact/Approx
AUTO or EXACT
Base
DEC
Language
ENGLISH
3. Press
¸. The Home screen displays.
MEMORY and VAR-LINK screens unavailable
The MEMORY and VAR-LINK screens, accessed by the 2¯
and 2°keys, are unavailable for the Calculus Tools App.
TI-89 dialog boxes
The TI-89 Calculus Tools App dialog boxes default to alpha-lock.
Press jto turn alpha-lock off before entering numbers.

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Using variables from the Main folder
Using variables from the Main folder places those stored values
in the Calculus Tools App functions. The Calculus Tools App,
however, clears the following types of variables for specified
functions. As a result, the data stored in these variables is lost.
Menu option
Variable defined as …
F2
F3
F4
F5
F6
Independent var
1 and 2;
4-7
4
Dependent var
4
Angle Parameter
7
Index var
1
Coordinate variables
All
Integration variables
5-8
Var n
2 and 3
x
3
All
Viewing answers in split screen
The Calculus Tools App uses a split screen view to display the
numerical and graphical representations of selected solutions.
•For answers that are partially hidden when viewed in a split
screen, press Nto view the answer in full screen.
•For answers that are too long to be viewed in a full screen,
use the Display Answer option.
•You cannot switch back and forth between the split screen
portions.

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Access the Calculus Tools App menus using the F1 through F6
function keys. F1 menu options let you change the configuration
of what you see on the screen, such as viewing the complete
answer or data entered as a string, changing split screen
settings, and restoring window defaults.
F2 through F6 menu options let you access calculus operations
and are organized under the broad categories of derivatives,
integrals, sequences, vectors, and advanced functions.
Most F2 through F6 options access a problem-entry dialog box
that includes an example problem to help you get started. Work
through the example problem, or replace it as desired.
Dialog boxes for most F2 through F6 menu options revert to
default values after data is entered. Dialog boxes for the F3
menu options, however, display the values entered last.
This is the problem-entry dialog box for 1:Tangent Line.

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F1:Tools
F1 1:Display ANSWER
Lets you view an answer that is too long to fit on the screen.
(Answers are displayed as a string.)
Tip
You can also go to the Home screen, type answer, and
press ¸. Scroll to see the complete answer displayed
in Pretty Print.

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F1 2:Display ENTERED
Lets you view executed commands or functions as a string,
including the Calculus Tools App functions and operations
entered from the problem-entry dialog box.
Tip
To run a Calculus Tools App function from the Home
screen, type entered and press ¸. The last command
(function and instructions) executed appears.
Be sure to remove the quotes from the string before
executing the command.

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F1 3:Change Split Screen
Lets you choose between left-right (default) and top-bottom
split screens.
The TI-92 Plus lets you change the ratio of the split screen
views.
•1:1 displays the answer and graph views at the same size.
•1:2 displays the answer view at half the size of the graph
view.
•2:1 displays the answer view at twice the size of the graph
view.

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F1 4:Restore Window Defaults
Restores the Calculus Tools App window parameters to
default values. Dialog boxes accessed using the F3 menu
options are also restored to default values.
Function Graph Window Parameters
Parameter
Default Value
xmin
-3.55102040816
xmax
3.55102040816
xscl
1
ymin
L3
ymax
3
yscl
1
xres
2
F1 5:Special Thanks
Acknowledges some of the Calculus Tools App contributors.
F1 6:About
Displays a variety of information about the application,
including the version number.

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F2:Deriv
F2 1:Tangent Line
Displays the problem-entry dialog box for the tanLine(...)
function along with an example problem (page 35).
F2 2:Normal Line
Displays the problem-entry dialog box for the prpendic(...)
function along with an example problem (page 34).

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F2 3:Newton’s Method
Displays the problem-entry dialog box for Newton's Method
along with an example problem. Enter a function f (x), Initial
guess, and Number of iterations.
Note
The number of iterations must be an integer 1.
The solution appears in a split screen. One portion of the split
screen displays a sequence of approximations to a real root
of the functions.
The other portion of the split screen displays a graph of the
function and draws tangent lines corresponding to
consecutive iterations.
The application draws the first guess for you. Press either
¸or Nto view the consecutive guesses. This example
shows four iterations.

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F2 4:Implicit Derivative
Displays the problem-entry dialog box for the impDifN(...)
function along with an example problem (page 32).
F2 5:Curvature
Displays the problem-entry dialog box for the curvatur(...)
function along with an example problem (page 31).

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F2 6:Center of Curvature
Displays the problem-entry dialog box for the cntrCurv(...)
function along with an example problem (page 30).
F2 7:Osculating Circle
Displays the problem-entry dialog box for the oscCircl(...)
function along with an example problem (page 33).

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F3:Integ
F3 1:Left Sum
Displays the problem-entry dialog box for the Left Sum
integration method along with an example problem. Enter a
function f (x), Lower bound, Upper bound, and Number of
intervals.
The answer appears in a split screen. One portion of the split
screen displays the sum of the areas of the rectangles.
The other portion of the split screen displays the graph of the
function and draws the rectangles.
F3 2:Right Sum
Displays the problem-entry dialog box for the Right Sum
integration method along with an example problem. Enter a
function f (x), Lower bound, Upper bound, and Number of
intervals.
The answer appears in a split screen. One portion of the split
screen displays the sum of the areas of the rectangles.

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The other portion of the split screen displays the graph of the
function and draws the rectangles.
F3 3:Midpoint Rule
Displays the problem-entry dialog box for the Midpoint Rule
along with an example problem. Enter a function f (x), Lower
bound, Upper bound, and Number of intervals.
The answer appears in a split screen. One portion of the split
screen displays the sum of the areas of the rectangles.
The other portion of the split screen displays the graph of the
function and draws the rectangles.

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F3 4:Trapezoidal Rule
Displays the problem-entry dialog box for the Trapezoidal
Rule along with an example problem. Enter a function f (x),
Lower bound, Upper bound, and Number of intervals.
The answer appears in a split screen. One portion of the split
screen displays the sum of the areas of the trapezoids.
The other portion of the split screen displays the graph of the
function and draws the trapezoids.
F3 5:Simpson’s Rule
Displays the problem-entry dialog box for Simpson's Rule
along with an example problem. Enter a function f (x), Lower
bound, Upper bound, and Number of intervals.
Note
The number of intervals must be an even integer 2.
The answer appears in a split screen. One portion of the split
screen displays the Simpson’s Rule approximation to the
definite integral by using parabolic arcs.

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The other portion of the split screen displays the graph of the
function and draws the parabolic arcs.
F3 6:Comparison
Returns the approximation to the definite integral using these
previously mentioned methods: Left Sum, Right Sum,
Midpoint Rule, Trapezoidal Rule, and Simpson’s Rule (pages
16 through 18).

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F4:Seq (infinite series, sequences)
F4 1:Ratio Convergence Test
Displays the problem-entry dialog box for the ratioTst(...)
function (page 34) along with an example problem.
F4 2:1st-Order Sequence
Displays the problem-entry dialog box for the seq1Solv(...)
function (page 34) along with an example problem.