This preview shows page 1. Sign up to view the full content.
Unformatted text preview: TI TI89 / TI92 Plus Calculus Tools Getting Started
W hat is the Calculus Tools Application? Before You Begin Starting the Calculus Tools Application Calculus Tools Menus
F1:Tools F2:Deriv F3:Integ F4:Seq F5:Vector F6:Advanced More Information
Calculus Tools Application Functions 8/10/01 © 2001 Texas Instruments Important Information
Texas Instruments makes no warranty, either expressed or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an "asis" basis. In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed any applicable purchase price of this item or material. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party. Graphing product applications (Apps) are licensed. See the terms of thelicense agreement for this product. TIGRAPH LINK is a trademark of Texas Instruments. All other trademarks are the property of their respective owners. TI89 / TI92 Plus Calculus Tools Page 2 What is the Calculus Tools Application?
The Calculus Tools application (App) is a Concept software application for the TI89 / TI92 Plus. Concept software applications are calculator software application prototypes that demonstrate a new concept area. The Calculus Tools App extends the builtin power of your TI89 / TI92 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.bkteachware.com. Other teaching and learning materials written for the TI89 and TI92 Plus are also available at the Web site, including Exploring Integration with the TI89/92/92+ by Josef Böhm and Wolfgang Pröpper.
TI89 / TI92 Plus Calculus Tools Page 3 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: TI89 / TI92 Plus Calculus Tools Page 4 1. From the Home screen, press 3 to display the MODE dialog box. 2. Ensure that the following modes are set as indicated:
Mode Graph Display Digits Angle Split Screen Exact/Approx Base Language Setting FUNCTION FLOAT or FLOAT # (1  12) RADIAN FULL AUTO or EXACT DEC ENGLISH Before starting the Calculus Tools App, set modes to the required values as follows: 3. Press ¸. The Home screen displays. MEMORY and VARLINK screens unavailable The MEMORY and VARLINK screens, accessed by the 2 ¯ and 2 ° keys, are unavailable for the Calculus Tools App. TI89 dialog boxes The TI89 Calculus Tools App dialog boxes default to alphalock. Press j to turn alphalock off before entering numbers.
TI89 / TI92 Plus Calculus Tools Page 5 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.
Variable defined as … Independent var Dependent var Angle Parameter Index var Coordinate variables Integration variables Var n x F2 1 and 2; 47 4 7 F3 Menu option F4 F5 F6 4 1 All 58 2 and 3 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 N to 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.
TI89 / TI92 Plus Calculus Tools Page 6 8VLQJ&DOFXOXV7RROV$SS0HQXV
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 problementry 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 problementry dialog box for 1:Tangent Line. TI89 / TI92 Plus Calculus Tools Page 7 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. TI89 / TI92 Plus Calculus Tools Page 8 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 problementry 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. TI89 / TI92 Plus Calculus Tools Page 9 F1 3:Change Split Screen Lets you choose between leftright (default) and topbottom split screens. The TI92 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. TI89 / TI92 Plus Calculus Tools Page 10 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 xmin xmax xscl ymin ymax yscl xres Default Value 3.55102040816 3.55102040816 1 3 1 2 L3 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. TI89 / TI92 Plus Calculus Tools Page 11 F2:Deriv F2 1:Tangent Line Displays the problementry dialog box for the tanLine(...) function along with an example problem (page 35). F2 2:Normal Line Displays the problementry dialog box for the prpendic(...) function along with an example problem (page 34). TI89 / TI92 Plus Calculus Tools Page 12 F2 3:Newton’s Method Displays the problementry 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 N to view the consecutive guesses. This example shows four iterations. TI89 / TI92 Plus Calculus Tools Page 13 F2 4:Implicit Derivative Displays the problementry dialog box for the impDifN(...) function along with an example problem (page 32). F2 5:Curvature Displays the problementry dialog box for the curvatur(...) function along with an example problem (page 31). TI89 / TI92 Plus Calculus Tools Page 14 F2 6:Center of Curvature Displays the problementry dialog box for the cntrCurv(...) function along with an example problem (page 30). F2 7:Osculating Circle Displays the problementry dialog box for the oscCircl(...) function along with an example problem (page 33). TI89 / TI92 Plus Calculus Tools Page 15 F3:Integ F3 1:Left Sum Displays the problementry 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 problementry 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.
TI89 / TI92 Plus Calculus Tools Page 16 The other portion of the split screen displays the graph of the function and draws the rectangles. F3 3:Midpoint Rule Displays the problementry 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. TI89 / TI92 Plus Calculus Tools Page 17 F3 4:Trapezoidal Rule Displays the problementry 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 problementry 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.
TI89 / TI92 Plus Calculus Tools Page 18 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). TI89 / TI92 Plus Calculus Tools Page 19 F4:Seq (infinite series, sequences) F4 1:Ratio Convergence Test Displays the problementry dialog box for the ratioTst(...) function (page 34) along with an example problem. F4 2:1stOrder Sequence Displays the problementry dialog box for the seq1Solv(...) function (page 34) along with an example problem. TI89 / TI92 Plus Calculus Tools Page 20 F4 3:2ndOrder Sequence Displays the problementry dialog box for the seq2Solv(...) function (page 35) along with an example problem. F5:Vector F5 1:Gradient Displays the problementry dialog box for the grad(...) function (page 32) along with an example problem. TI89 / TI92 Plus Calculus Tools Page 21 F5 2:Divergence Displays the problementry dialog box for the div(...) function (page 31) along with an example problem. Note The number of components in exprList must equal the number of variables in varList. F5 3:Curl Displays the problementry dialog box for the curl(...) function (page 30) along with an example problem. TI89 / TI92 Plus Calculus Tools Page 22 F5 4:Potential Displays the problementry dialog box for the potentl(...) function (page 33) along with an example problem. F6:Advanced F6 1:Error Function, erf Displays the problementry dialog box for the erf(...) function (page 31) along with an example problem. TI89 / TI92 Plus Calculus Tools Page 23 F6 2:Comp. Error Function Displays the problementry dialog box for the erfc(...) function (page 31) along with an example problem. F6 3:Gamma Function Displays the problementry dialog box for the gamma(...) function (page 32) along with an example problem. TI89 / TI92 Plus Calculus Tools Page 24 F6 4:Fourier Series Displays the problementry dialog box for the fourirCf(...) function (page 32) along with an example problem. F6 5:Integral of Density F6 5:Integral of Density > 1:over a Surface Displays the problementry dialog box for the surfIntg(...) function (page 35) along with an example problem. TI89 / TI92 Plus Calculus Tools Page 25 F6 5:Integral of Density > 2:over a Polar Region Displays the problementry dialog box and example problem to set up an iterated integral to integrate a density over a region in polar coordinates. Use density 1 for an unweighted polar area. F6 6:Centroid of Density Displays the problementry dialog box for the aCntroid(...) function (page 29) along with an example problem. TI89 / TI92 Plus Calculus Tools Page 26 F6 7:Inertia Tensor Displays the problementry dialog box for the aInertia(...) function (page 30) along with an example problem. F6 8:Arc Displacement Displays the problementry dialog box for the plrArcLn(...) function along with an example problem (page 33). TI89 / TI92 Plus Calculus Tools Page 27 Working with Calculus Tools App Functions
Use Calculus Tools App functions outside the application when working with programs or other builtin, userdefined, and Flash application functions.
Note Calculus Tools App functions cannot be called from within the application. If you try to call a function using the application’s problementry dialog boxes, the error message, Protected memory violation, will appear. Exit and reenter the application to ensure normal operation. Accessing Calculus Tools App functions from the Catalog 1. From the Home screen, press ½ (TI89) / (TI92 Plus). The catalog appears. 2. Press c. The list of Flash application functions appears. 3. Scroll through the list and select the function you want to use. 4. Press ¸. The function appears on the Home screen entry line in the form CalcTool.function name 5. Add the required arguments to complete the command and press ¸.
Tip To view help for a function, select a function from the catalog and press . TI89 / TI92 Plus Calculus Tools Page 28 1. From the Home screen, press 2 °. The VARLINK [ALL] screen appears. 2. Press 2 (TI89) / g (TI92 Plus). The list of Flash application functions appears. 3. Scroll through the list and select the function you want to use. You may need to expand the application's folder before you can view its functions. 4. Press ¸. The function appears on the entry line as CalcTool.function name 5. Add the required arguments to complete the command and press ¸. List of Calculus Tools App Functions aCntroid(density, var1, lower1, upper1, var2, lower2(var1), upper2(var1)) Returns a twoelement list denoting the {var1, var2} coordinates of the centroid of a density over a 2D region. var1 varies from lower1 to upper1, which must be independent of var1 and var2. var2 varies from expression lower2 to expression upper2, which might depend on var1. Use density 1 for an area centroid. Use F6 6:Centroid of Density to display the problementry dialog box and example for this function. Accessing Calculus Tools App functions from VARLINK TI89 / TI92 Plus Calculus Tools Page 29 alnertia(density, var1, lower1, upper1, var2, lower2(var1), upper2(var1)) Returns a 2x2 matrix denoting the inertia tensor of a density over a twodimensional region. var1 varies from lower1 to upper1, which must be independent of var1 and var2. var2 varies from expression lower2 to expression upper2, which might depend on var1. Use density 1 for an area inertia tensor. Use F6 7:Inertia Tensor to display the problementry dialog box and example for this function.
cntrCurv(expression, var) Returns a twoelement list that is a parametric representation of the center of curvature of expression with respect to var. Use F2 6:Center of Curvature to display the problementry dialog box and example for this function.
curl(exprList, xVar, yVar, zVar) Returns the threedimensional rectangular Cartesian curl of the vector represented by exprList with respect to the coordinate variables xVar, yVar, zVar. Use F5 3:Curl to display the problementry dialog box and example for this function. TI89 / TI92 Plus Calculus Tools Page 30 curvatur(expression, var) Returns the curvature of expression with respect to var. Use F2 5:Curvature to display the problementry dialog box and example for this function.
div(exprList, varList) Returns the rectangular Cartesian ndimensional divergence of the vector represented by exprList with respect to the n coordinate variables in VarList. Use F5 2:Divergence to display the problementry dialog box and example for this function.
Note The number of components in exprList must equal the number of variables in varList. erf(complexNumber) Returns the approximate numeric error function of complexNumber. Use F6 1:Error Function, erf to display the problementry dialog box and example for this function.
erfc(complexNumber) Returns the approximate complementary error function of complexNumber.
TI89 / TI92 Plus Calculus Tools Page 31 Use F6 2:Comp. Error Function to display the problementry dialog box and example for this function.
fourirCf(expression, var, lowerLimit, upperLimit, n) Returns the truncated Fourier series of expression for var from lowerLimit to upperLimit, through the nth harmonic. Use F6 4:Fourier Series to display the problementry dialog box and example for this function.
gamma(complexNumber) Returns the approximate gamma function of complexNumber. Use F6 3:Gamma Function, Γ(z) to display the problementry dialog box and example for this function.
grad(expression, VarList) Returns the rectangular Cartesian ndimensional gradient of expression with respect to the n coordinate variables in VarList. Use F5 1:Gradient to display the problementry dialog box and example for this function.
impDifN(equation, IndependentVar, DependentVar, n) Returns the nth derivative of the function implicitly defined by equation. Use F2 4:Implicit Derivative to display the problementry dialog box and example for this function.
TI89 / TI92 Plus Calculus Tools Page 32 oscCircl(expression, var, circleParameter) Returns a twoelement list that is a parametric representation of the circle that osculates expression. Use F2 7:Osculating Circle to display the problementry dialog box and example for this function. plrArcLn(r(GVar), GVar, low, up, weight(GVar)) Returns the weighted arc displacement in polar coordinates, where var GVar varies from lowerLimit to upperLimit, with r(GVar) and weight(GVar) being expressions that might depend on GVar. Use weight 1 for an unweighted arc displacement. Use F6 8:Arc Displacement to display the problementry dialog box and example for this function.
potentl(exprList, xVar, yVar, zVar, x0, y0, z0) Returns the scalar potential of the threedimensional rectangular Cartesian gradient represented by exprList, with the potential = 0 at {x0, y0, z0}.
Note Does not verify that exprList is a gradient, so first see if curl(exprList, xVar, yVar, zVar) simplifies to {0,0,0}, as it should for a gradient. Use F5 4:Potential to display the problementry dialog box and example for this function. TI89 / TI92 Plus Calculus Tools Page 33 prpendic(expression, var, varValue) Returns an expression for the line that is normal to expression at var = varValue. Use F2 2:Normal Line to display the problementry dialog box and example for this function.
ratioTst(expression, indexVar) Conducts the ratio test for the convergence of an infinite series, returning one of the strings converges, diverges, test inconclusive, or unable to complete test. Use F4 1:Ratio Convergence Test to display the problementry dialog box and example for this function.
seq1Solv(p(n), r(n), n, nMin, ui) Attempts to return an exact symbolic expression for u(n) that satisfies the linear 1storder sequence equation u(n)=p(n)
u(n1)+r(n) with u(nMin)=ui. Use F4 2:1stOrder Sequence to display the problementry dialog box and example for this function. TI89 / TI92 Plus Calculus Tools Page 34 seq2Solv(k, c, r(n), n, nMin, {u(nMin), u(nMin1)}) Attempts to return an exact symbolic expression for u(n) that satisfies the linear 2ndorder constantcoefficient sequence equation u(n)=k
u(n1)+c
u(n2)+r(n) and ui={u(nMin) , u(nMin1)}. Use F4 3:2ndOrder Sequence to display the problementry dialog box and example for this function.
surfIntg(density, height, var1, lower1, upper1, var2, lower2(var1), upper2(var1)) Returns the integral of a density over surface whose height might vary with var1 and var2. var1 varies from lower1 to upper1, which must be independent of var1 and var2. var2 varies from expression lower2 to expression upper2, which might depend on var1. Use density 1 for a surface area. Use F6 5:Integral of Density > 1:over a Surface to display the problementry dialog box and example for this function.
tanLine(expression, var, varValue) Returns an expression for the line that is tangent to expression at var = varValue. (In contrast, the builtin LineTan command draws the tangent line but does not reveal its formula.) Use F2 1:Tangent Line to display the problementry dialog box and example for this function. TI89 / TI92 Plus Calculus Tools Page 35 Installing the Calculus Tools App
Detailed Flash application installation instructions are available from education.ti.com/guides. You will need: • A TI89 / TI92 Plus with the latest Advanced Mathematics Software Operating System. Download a free copy from education.ti.com/softwareupdates. • A computer using either Microsoftë Windowsë or Appleë Macintoshë operating system software. • A TIGRAPH LINK™ computertocalculator cable, available for purchase from the TI Online Store at education.ti.com/buy. • TIGRAPH LINK connectivity software for the TI89 / TI92 Plus. Download a free copy from education.ti.com/softwareupdates. TI89 / TI92 Plus Calculus Tools Page 36 Starting and Quitting the Application
Starting the Calculus Tools App The instructions in this guidebook refer to this Flash application only. For help using the TI89 / TI92 Plus, refer to the comprehensive guidebook at education.ti.com/guides. 2. Press 1:FlashApps and select Calculus Tools. 3. Press ¸. The Hint screen displays. 1. Ensure modes are set to the required values. Quitting the Calculus Tools App Press 2 K from the Calculus Tools App Hint screen. TI89 / TI92 Plus Calculus Tools Page 37 Deleting an Application
Deleting an application removes it from the calculator and increases space for other applications. Before deleting an application, consider storing it on a computer for reinstallation later. 1. Quit the application. 2. Press 2 ° to display the VARLINK [ALL] screen. 3. Press 2 (TI89) / (TI92 Plus) to display the list of applications. 4. Select the application you want to delete. 5. Press 1:Delete. The VARLINK delete confirmation dialog box displays. 6. Press ¸ to delete the application. TI89 / TI92 Plus Calculus Tools Page 38 Concept Application Evaluation License Agreement
(Including Preview, Prototype, and Demo APPS)
By downloading the software and/or documentation you agree to abide by the following provisions.
1. Copyright: The Licensed Materials are copyrighted by TI or the third party licensor. Licensee agrees that he/she will not delete the copyright notice, trademarks or protective notices from the Licensed Materials or copies made during installation. Support: The Licensed Materials are provided by TI with the understanding that only limited support for this concept application may be available from TI. Testing: Licensee acknowledges that he/she understands that TI has not in all cases subjected concept applications to rigorous testing and that the concept application may cause problems with his/her calculator, including its use in any kind of shared environment. Further, it is possible for a concept application to cause calculator crashes or lock ups which may be difficult to recover from. You are advised that use of the concept application is AT YOUR OWN RISK. Warranty: TI does not warrant that the Licensed Materials will be free from errors or will meet your specific requirements. The Licensed Materials are made available "AS IS" to Licensee. Limitations: TI makes no warranty or condition, either express or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding the Licensed Materials. In no event shall TI, any third party licensor, or TI's suppliers be liable for any indirect, incidental or consequential damages, loss of profits, loss of use or data, or interruption of business, whether the alleged damages are labeled in tort, contract or indemnity. Some states do not allow the exclusion or limitation of incidental or consequential damages, so the above limitation may not apply. 6. Restricted Rights: The Licensed Materials are provided with Restricted Rights. Use, duplication or disclosure by the United States Government is subject to restrictions as set forth in subparagraph [c](1)(ii) of the Rights in Technical Data and Computer Software clause at DFARS 252.2277013 or in subparagraph [c](1) and (2) of the Commercial Computer Software  Restricted Rights at 48 CFR 52.22719, as applicable. 2. 3. 4. 5. TI89 / TI92 Plus Calculus Tools Page 39 Page Reference This PDF document contains electronic bookmarks designed for easy onscreen navigation. If you decide to print this document, please use the page numbers below to find specific topics.
Important Information............................................................................................. 2 W hat is the Calculus Tools Application?................................................................ 3 Before You Begin ................................................................................................... 4 Mode settings .................................................................................................... 4 MEMORY and VARLINK screens inactive ....................................................... 5 TI89 dialog boxes ............................................................................................. 5 Using variables from the Main folder ................................................................. 6 Viewing answers in split screen......................................................................... 6 Using Calculus Tools App Menus .......................................................................... 7 F1:Tools............................................................................................................. 8 F2:Deriv ........................................................................................................... 12 F3:Integ............................................................................................................ 16 F4:Seq (infinite series, sequences) ................................................................. 20 F5:Vector ......................................................................................................... 21 F6:Advanced.................................................................................................... 23 W orking with Calculus Tools App Functions........................................................ 28 Accessing Calculus Tools App functions from the Catalog ............................. 28 Accessing Calculus Tools App functions from VARLINK............................... 29 List of Calculus Tools App Functions .............................................................. 29 Installing the Calculus Tools App ......................................................................... 36 Starting and Quitting the Application .................................................................... 37 Starting the Calculus Tools App ...................................................................... 37 Quitting the Calculus Tools App ...................................................................... 37 Deleting an Application......................................................................................... 38 Concept Application Evaluation License Agreement ........................................... 39 TI89 / TI92 Plus Calculus Tools Page 40 ...
View
Full
Document
This note was uploaded on 04/04/2011 for the course MAC 2311 taught by Professor Baird,j during the Spring '08 term at Hillsborough.
 Spring '08
 Baird,J
 Calculus

Click to edit the document details