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Casio CLASSPAD330PLUS 14-3Graphing a Second Order Differential Equation, Drawing the Phase Plane of a Second Order Differential Equation, 9Xw-Yw

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14-3-1

Graphing a Second Order Differential Equation

14-3 Graphing a Second Order Differential Equation

This section explains how to input a second order differential equation and draw a slope field, and how to graph the solution curve(s) for a second order differential equation based on given initial conditions.

With this application, a second order differential equation is input in the form of a set of two first order differential equations.

Drawing the Phase Plane of a Second Order Differential Equation

A phase plane is the family of solutions of either a second order differential equation or two first order differential equations of the form x’ = dx/dt = f(x,y) and y’ = dy/dt = g(x,y). A single second order differential equation can also be graphed, but it must be written as two first order differential equations.

Example: To input {x’ = x, y’ = −y} and draw its phase plane

uClassPad Operation

(1)On the application menu, tap .

•This starts up the Differential Equation Graph application and activates the differential equation editor ([DiffEq] tab).

(2)Tap [Type] - [2nd (Phase Plane)] or the B toolbar button.

(3)Use the differential equation editor to input x’ = x, y’ = −y.

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Contents

ClassPad OS Version Software User’s Guide Contents 1-8Using the Variable Manager 2 Using the Main Application Main Application Overview Basic Calculations List Calculations Matrix and Vector Calculations 2-9Using the Interactive Menu 2-10Using the Main Application in Combination with Other Applications 2-11Using Verify Using Probability 3 Using the Graph & Table Application Storing Functions Using Table & Graph Using Trace Analyzing a Function Used to Draw a Graph 4 Using the Conics Application Inputting Equations Drawing a Conics Graph Using Trace to Read Graph Coordinates Using G-Solveto Analyze a Conics Graph Chapter 6 Using the Sequence Application 6-2Inputting an Expression in the Sequence Application Recursive and Explicit Form of a Sequence Using LinkTrace 7 Using the Statistics Application Chapter 8-4Controlling Geometry Window Appearance Working with Animations Using the Geometry Application with Other Applications 9 Using the Numeric Solver Application Numeric Solver Application Overview 10-5Transferring eActivity Files Chapter 11 Using the Presentation Application Building a Presentation Managing Presentation Files Configuring Presentation Preferences 12-6Program Command Reference 12-7Including ClassPad Functions in Programs Chapter 13 Using the Spreadsheet Application Spreadsheet Application Overview 13-2Spreadsheet Application Menus and Buttons Using the Spreadsheet Application with the eActivity 13-7Cell and List Calculations Graphing Chapter 14 Using the Differential Equation Graph Application 14-1Differential Equation Graph Application Overview 14-6Configuring Differential Equation Graph View Window 14-7Differential Equation Graph Window Operations Chapter 15 Using the Financial Application 15-1Financial Application Overview 15-2Simple Interest 15-17Performing Financial Calculations Using Commands Chapter 16 Configuring System Settings 16-1System Setting Overview Using the Reset Dialog Box Initializing Your ClassPad Appendix α-1-1 α-2-1 α-3-1 α-4-1 About This User’s Guide ClassPad Keypad and Icon Panel z ^ 1Keypad Example 1: On-screenKeys, Menus, and Other Controllers 4 Menu bar 5Toolbar 6 Soft keyboard Example 1: baa/gw Important Page Contents Note Getting Acquainted 1-1General Guide General Guide Front 1Touch screen 2Stylus 3Icon panel Side !3-pindata communication port @4-pinmini USB port Back #Battery compartment Using the Stylus kThings you can do with the stylus Tap Drag 1-2Turning Power On and Off 1-3Using the Icon Panel 1-4 Built-inApplications • Control the optionally available EA-200 Data Analyzer • Exchange data with another ClassPad a computer, or another device Starting a Built-inApplication Perform the steps below to start a built-inapplication u ClassPad Operation (1) On the icon panel, tap mto display the application menu Application Menu kUsing Application Groups To display these icons: Select this application group: Add-inapplications only Additional uClassPad Operation kSwapping Two Icons kAdjusting Touch Panel Alignment 1-5 Built-inApplication Basic Operations uTo switch the active window uTo resize the active window so it fills the display uTo swap the upper and lower windows uTo close the active windows Using the Menu Bar Using the OMenu k OMenu Items k Using the OMenu to Access Windows uWindow Selection Example (Graph & Table) Using Check Boxes Using Option Buttons Using the Toolbar kToolbar Buttons kToggling between Multiple Toolbars Interpreting Status Bar Information The status bar appears along the bottom of the window of each application 1 Information about current application 2 Battery level indicator ....................... full kTerminating an Operation (Break) 1-6Input 1-6-2Input kSoft Keyboard Styles There are four different soft keyboard styles as described below •Math (mth) Keyboard •Alphabet (abc) Keyboard •Catalog (cat) Keyboard kSelecting a Soft Keyboard Style Input Basics kInputting a Calculation Expression kEditing Input The following are the different techniques you can use to edit your input uTo change something right after you input it Example: To change the expression 369 ⋅ 3 to 369 ⋅ (1) c369*3 uTo delete an unneeded key operation Example: To change the expression 369 ⋅ ⋅ 2 to 369 ⋅ (1) c369**2 (2) dK uTo correct a calculation expression uTo insert new input into the middle of an existing calculation expression Example: To change 2.362 to sin(2.362) (1) c9c.dgx (2) dddddd (3) Ts kUsing the Clipboard for Copy and Paste uTo copy characters (1)Drag the stylus across the characters you want to copy to select them (2)On the soft keyboard, tap G •This puts a copy of the selected characters onto the clipboard Advanced Soft Keyboard Operations kUsing the Math (mth) Keyboard u Initial math (mth) keyboard key set 1-6-9Input u Tkey set u - key set u K key set u K kUsing the Alphabet (abc) Keyboard u Initial alphabet (abc) keyboard key set u Mkey set u n key set u Skey set kUsing Single-characterVariables uTo input a single-charactervariable name •Tapping any key in the math (mth) keyboard’s V key set (page 1-6-10) •Tapping any key in the 2D keyboard’s V key set (page 1-6-17) Tapping the uTo input a series of multiple characters Example: 0abcw Example: 0a*b+cw kUsing the Catalog (cat) Keyboard u Catalog (cat) keyboard configuration uTo use the catalog (cat) keyboard Example: To input the built-in“Plot” command (1)Tap (to display the catalog (cat) keyboard Tap the “Form” down arrow button (3)Tap the ubutton in the lower right corner until the P key is visible kUsing the 2D Keyboard u Initial 2D keyboard key set To input this: Use these keys: For more information, see: u ADV key set uTo use the 2D keyboard for natural input Example 1: To input 1 + To input (1)On the application menu, tap Jto start the Main application (2)Press the ckey Example 2: To input k2 (1)Tap )to display the 2D keyboard and then tap (2)Tap (3)In the input box below Σ, input “k=1” Vkeb Page 1-7Variables and Folders kCurrent Folder Variable Types Variable Type kVariable Data Types data types data type name Data Type Name Data Type Creating a Folder kCreating a folder using the Variable Manager kCreating a folder using the “NewFolder” command kFolder Name Rules The following are the rules that apply to folder names •Folder names can be up to 8 bytes long •The following characters are allowed in a folder name Underscore (character code 95) kSingle-characterVariable Precautions kCreating a New Variable kVariable Usage Example k“library” Folder Variables kUsing Stat Editor to Create a LIST Variable • For details about using Stat Editor, see “7-2Using Stat Editor” Assigning Values and Other Data to a System Variable system variable Locking a Variable or Folder •Locking a folder makes it impossible to delete or rename the folder uTo lock or unlock a variable or folder using the Variable Manager Rules Governing Variable Access kVariable Search Priority Sequence (1)Local Variables (2)Current Folder Variables (3)“library” Folder Variables 1-8Using the Variable Manager Variable Manager Views Exiting the Variable Manager Variable Manager Folder Operations kSpecifying the Current Folder You can also select a folder you created yourself as the current folder kCreating a New Folder kSelecting and Deselecting Folders Do this: Select a single folder Select the check box next to the folder name Deselect a single folder kRenaming a Folder You can use the following procedure to change the name of an existing folder kLocking and Unlocking a Folder uTo lock a folder (2)Select the check box next to the folder you want to lock kInputting a Folder Name into an Application Variable Operations kOpening a Folder kOpening the “library” Folder kDisplaying a List of a Particular Type of Variable kSelecting a Variable uTo select or deselect a variable Perform one of the operations described below to select or deselect a variable Select a single variable Select the check box next to the variable name kDeleting a Variable Perform the following steps when you want to delete a variable kCopying and Moving a Variable You can use the procedure below to copy or move a variable to another folder kRenaming a Variable Perform the following steps when you want to rename a variable kLocking and Unlocking a Variable uTo lock a variable (2)Select the check box next to the variable you want to lock uTo unlock a variable (2)Select the check box next to the variable you want to unlock kSearching for a Variable kViewing the Contents of a Variable You can use the Variable Manager to view the contents of a particular variable kInputting a Variable Name into an Application 1-9Configuring Application Format Settings Specifying a Variable (6)Tap [OK] •This closes the Select Data dialog box (7) Tap [Set] to save your settings Initializing All Application Format Settings (1)Tap O, or tap son the icon panel, and then tap [Default Setup] Application Format Settings kBasic Format Dialog Box uCurrent Folder To specify this folder as the current folder: Select this setting: uNumber Format To specify this type of numeric value display format: uAngle To specify this angle unit: uAdvanced kGraph Format Dialog Box Basic Tab uAxes uOther settings Special Tab uBackground uCell Width Pattern To specify this row width for stat editor and data table displays: k3D Format Dialog Box uCoordinates Select this setting: Select the kGeometry Format Dialog Box To specify this type of numeric value display format on the Geometry window: uMeasure Angle To specify the angle unit for the measurement box: uFunction Angle kAdvanced Format Dialog Box uFourier Transform uFFT uAssume positive real kFinancial Format Dialog Box Page kPresentation Dialog Box kCommunication Dialog Box uScreen Copy To To do this with hard copy data generated by tapping h: Using the Main Application 2-1Main Application Overview Page Main Application Menus and Buttons Menu Commands menu item: Button Functions Tap this button: Using Main Application Modes kStatus Bar Mode Indicators Status Bar Indicator Setting Accessing ClassPad Application Windows from the Main Application To display this window: Tap this button: Graph & Table application Graph window Accessing the Main Application Window from Another ClassPad Application •Using drag and drop to copy expressions and values between windows 2-2Basic Calculations Using the eKey Examples: Omitting the Multiplication Sign Using the Answer Variable (ans) kPerforming Continuous Calculations Example: 1 ÷ 3 1 ÷ 3 1 ÷ 3 × 3 = cb/dw (Continuing)*dw Continuous calculations can be used with +, –, ⋅, ÷, and ^ Assigning a Value to a Variable Syntax: Variable: = value Example: Assign 123 to variable (1) Perform the key operation below in the Main application work area 9X0L:9=bcd Calculation Priority Sequence 2Factorials (x!), degree specifications (o, r ), percents (%) 3Powers 5+, –, (–) 6Relational operators (=, ≠, <, >, <, >) Calculation Modes kStandard Mode and Decimal Mode uExamples of Decimal mode and Standard mode result displays Decimal Mode Result uUsing the uButton to Toggle between the Standard Mode and Decimal Mode ClassPad Operation Displayed Result uNumber of Decimal Places, Number of Significant Digits, Normal Display uExamples of Complex mode and Real mode calculation results Complex Mode Real Mode solve (x3 – x2 + x – 1 = 0, x) {x = –i, x = i, x = 1} 2-3Using the Calculation History Re-calculatingan Expression (1)Move the cursor to the location from which you want to re-calculate •In this example, we will tap the end of line 2 to locate the cursor there (2)Tap “Standard” on the status bar to toggle it to “Decimal” Deleting Part of the Calculation History Contents Clearing All Calculation History Contents 2-4Function Calculations kTrigonometric Functions (sin, cos, tan) and Inverse Trigonometric Functions (sin–1, cos–1, tan–1) sin63° Func s 63 w kLogarithmic Functions (log, ln) and Exponential Functions (e, ^, k) l 1.23 w or )V10 e 1.23 w )V0ne )V3 e 9 w =13.6 w =21.5 )-11.5 =@20 / 15 w or =@)N 20 c 15 w 1500 * 12 &w 660 / 880 &w 2500 *( 1 + 15 & 3500 *( 1 - 25 & )52 e+55 w kRandom Number Generator (rand, randList, randNorm, randBin, RandSeed) u“rand” Function “randList” Function Description: u“randNorm” Function u“randBin” Function u“RandSeed” Command Generate sequential random [RandSeed] 3 w numbers using 3 as the seed value u“iLcm” Function u“iMod” Function kPermutation (nPr) and Combination (nCr) uTotal Number of Permutations uTotal Number of Combinations kCondition Judgment (judge, piecewise) u“judge” Function u“piecewise” Function 2 w kAngle Symbol (∠) kDerivative Symbol (’) kPrimality Test (isPrime) kEqual Symbols and Unequal Symbols (=, ≠, <, >, , >) You can use these symbols to perform a number of different basic calculations To add 3 to both sides of (X= 3 )+ 3 w x Solution Example kDirac Delta Function Syntax: delta(x) knth Delta Function kHeaviside Unit Step Function kGamma Function (n) = undefined, n Syntax: gamma(x) 2-5List Calculations kLIST Variable Element Operations kInputting List Data Using the Stat Editor Window Using a List in a Calculation kList Calculation Errors kList Calculation Example Using a List to Assign Different Values to Multiple Variables Sintaxis: List with Numbers S List with Variables 9{ba,ca,da}W{X,Y,Z} 2-6Matrix and Vector Calculations ClassPad Operation value “5” to the element at row 1 column 2 in “mat1”, which produces the matrix You can recall the value of any element of a MATRIX variable. When the data Matrix Variable Element Operations (1)Recall the value in row 2, column 1 of MATRIX variable “mat1” kInputting Matrix Values with the )Keyboard Tap this 2D key: Performing Matrix Calculations kMatrix Addition, Subtraction, Multiplication, and Division Page kRaising a Matrix to a Specific Power Example: To raise To raise to the power of The following are the screens that would be produced by each input method 2-7Specifying a Number Base Page Selecting a Number Base uTo select the number base for the line where the cursor is located Number System Suffix uTo specify a number base for an input value Arithmetic Operations Example 1: To calculate 101112 + (1)Tap the down arrow button next to the <button, and then tap (2)Perform the following key operation Bitwise Operations Operator and xor Example 4: 2-8Using the Action Menu Example Screenshots When the input expression does not fit: When the output expression does not fit: Displaying the Action Menu Using the Transformation Submenu uapprox usimplify uexpand ufactor urFactor ufactorOut ucombine ucollect utExpand utCollect uexpToTrig utrigToExp utoFrac upropFrac udms utoDMS L[ f(t)] (s)=∫0∞ f(t)e–stdt x’ + 2x = e–t where x(0) The Fourier Transform pairs are defined using two arbitrary constants a, b ⏐b⏐ ∫– ∞ f(t)eibωt dt ∫– ∞ F(ω)e–ibωt dω n (optional) Definition of the Fourier Integral f(x) = ∫–∞ F(k)e2πikx dk F(k) = ∫–∞ f(x)e–2πikx dx H(ω) = F [h(t)] = ∫–∞ h(t)e–iωt dt ⏐b⏐ ibωt ∫–∞ F –ibωt Using the Calculation Submenu udiff uimpDiff tol ulim urangeAppoint umod utanLine unormal uarcLen ufMin ufMax ugcd ulcm udenominator unumerator Using the Complex Submenu uarg uconjg ure uim ucExpand ucompToPol ucompToTrig ucompToRect Using the List-CreateSubmenu useq uaugment ufill usubList ushift urotate usortA usortD ulistToMat umatToList Using the List-CalculationSubmenu umin umax umean umedian umode uQ1 uQ3 upercentile ustdDev uvariance udim usum uprod ucuml uAlist upercent upolyEval usequence usumSeq Using the Matrix-CreateSubmenu utrn uident usubMat udiag Using the Matrix-CalculationSubmenu udet unorm urank uref urref ueigVl ueigVc uLU uQR uswap umRow umRowAdd urowAdd urowDim urowNorm ucolDim ucolNorm Using the Vector Submenu uunitV uangle ucrossP udotP utoRect x y x y z utoPol utoSph utoCyl Using the Equation/Inequality Submenu Page urewrite uexchange ueliminate uabsExpand uandConnect ugetRight ugetLeft uand uor uxor unot Using the Assistant Submenu uarrange ureplace uinvert uClear_a_z Using the Distribution and Inv. Distribution Submenus Specifying Arguments within the Distribution Function normPDf(1, 1, 0) normPDf({1, 2}, 1, 0) = {0.24, 0.05} unormPDf unormCDf uinvNormCDf utPDf utCDf uinvTCDf uchiPDf uchiCDf uinvChiCDf ufPDf ufCDf uinvFCDf ubinomialPDf pos ubinomialCDf uinvBinomialCDf xInv upoissonPDf upoissonCDf uinvPoissonCDf ugeoPDf ugeoCDf uinvGeoCDf uhypergeoPDf uhypergeoCDf uinvHypergeoCDf Using the Financial Submenu Simple Interest usimpInt usimpFV Compound Interest ucmpdFV ucmpdN ucmpdPmt ucmpdPV Cash Flow (Investment Appraisal) ucashIRR ucashNFV ucashNPV ucashPBP Amortization uamortBal uamortInt uamortPrn uamortSumInt uamortSumPrn Interest Conversion uconvEff uconvNom Cost/Sell/Margin upriceCost upriceMargin Day Count udayCount Bond Calculation ubondPriceDate ubondYieldDate ubondYieldTerm Using the Command Submenu uDefine uDispStat 2-9Using the Interactive Menu uTo factorize from the Action menu Page Using the “apply” Command 2-10Using the Main Application in Combination with Other Applications Closing Another Application’s Window (1)Tap anywhere inside of the window you would like to close (2)Tap the Sbutton in the upper right corner, or tap Oand then [Close] • The Main application work area expands to fill the entire display Using the Graph Window $and 3D Graph Window % (3)Drag the stylus across “x^2 – 1” in the work area to select it (4)Drag the selected expression to the Graph window •This graphs y = x2 – 1. This graph reveals that the x-interceptsare x = ±1 Using a Graph Editor Window (Graph & Table: !, Conics: *, 3D Graph: @, Numeric Solver: 1) (4)Press Eto register the expression •You could now tap $to graph the function Using the Stat Editor Window kExample List Operation Page Page (7)Tap the Stat Editor window to make it active (9)Tap the blank cell next to “list6”, input “test”, and then tap w Using the Geometry Window kDragging an Expression from the Work Area to the Geometry Window Page kDragging a Figure from the Geometry Window to the Work Area Dropping this into the work area: Displays this: Coordinates as a vector (2 ⋅ 1 matrix) Line 2-11Using Verify Verify Menus and Buttons kFile Menu Select this File Discard the current window contents and create a new file New kVerify Buttons Tap this Verify button: Using Verify Page 2-12Using Probability Starting Up Probability Use the following procedure to start up Probability (2)On the icon palette that appears, tap P (3)Tap [OK] Probability Menus and Buttons kDisplay Menu Select this Display Show the selected result distribution table format Distribution Show the selected result as a list data format Using Probability Page Page 2-13Running a Program in the Main Application Page 3-1Graph & Table Application Overview 3-2Using the Graph Window 3-3Storing Functions 3-4Using Table & Graph 3-5Modifying a Graph 3-1Graph & Table Application Overview Graph & Table Application Menus and Buttons k Graph Editor Window Menus and Buttons Or select this Page k Graph Window Menus and Buttons ∫dx π ∫ k Table Window Menus and Buttons Graph & Table Application Status Bar Angle unit Real mode If you see this: The angle unit setting is radians Example 1: To input the function y = 3x2 on Sheet 1 and graph it (1)On the application menu, tap T •This starts the Graph & Table application •This locates the cursor in the input box for line y1 (3)Input the expression (4)Tap $ • This graphs the expression The expression is displayed in the message box while the graph is being drawn Page Page 3-2Using the Graph Window You can also use the rectangular coordinate View Window dialog box to select To select this type of graph: x-loggraph Select the x-logcheck box • This automatically sets “xdot” and uView Window parameter precautions uTo initialize View Window parameters uTo initialize the View Window for an angle unit uTo standardize the View Window xmin = –10 ymin = –10 tmax uTo auto configure View Window parameters uTo recall a setup from View Window memory (4)Select the name of the setup you want, and then tap [OK] Viewing Graph Window Coordinates Scrolling the Graph Window •Tap the graph controller arrows at the edges of the Graph window •Use the cursor key Panning the Graph Window (1)Tap the Graph window to make it active Zooming the Graph Window k Zoom Commands Zoom Command uTo use box zoom Box Zoom Result uTo use factor zoom (6)Input 5 for both the xFactor and yFactor, and then tap [OK] (8)Tap [Zoom] and then [Zoom In] Factor Zoom Result k Using Quick Zoom Command View Window Parameter Values –7.7 k Using Other Zoom Menu Commands For information about what each command does, see “Zoom Commands” on page k Saving a Screenshot of a Graph uTo save a screenshot of a graph (2)Draw the graph you want to save k Redrawing a Graph k Making the Graph Editor Window the Active Window 3-3Storing Functions k Returning Sheets to Their Default Names k Initializing a Sheet Specifying the Function Type y xt/yt uTo store a rectangular coordinate function (Y=) uTo store a polar coordinate equation (r=) uTo store parametric functions uTo store an x = equation Example: To store x = 3y in line (2)Tap the box to the right of line number “x4”, and then input the equation: 3y (3)Press Eto store the equation Using Built-inFunctions y = a·x + b y = a·x^2 + b·x + c a·x^ b·x^ uTo save an expression from the message box to the Graph Editor window Perform a Trace operation (see (4)Tap G (5)Tap the Graph Editor window to make it active (7)Tap [Edit] and then [Paste] Deleting All Graph Editor Expressions Graphing a Stored Function k Specifying the Function You Want to Graph k Specifying the Graph Line Style Thick Broken Thick Square Plot Type k Quick Graphing of an Expression Using Drag and Drop k Overlaying Two Inequalities in an AND Plot / OR Plot •AND Plot With an AND Plot, only the parts of the inequalities that overlap are shaded •OR Plot Page k Shading the Region Bounded by Two Expressions k Using the Draw Shade Dialog Box to Shade the Region Bounded by Two Expressions k Dropping an Expression from the Main Application Work Area into the Graph Window Saving Graph Editor Data to Graph Memory uTo save Graph Editor data to graph memory uTo recall a graph memory file 3-4Using Table & Graph uTo generate a number table by specifying a range of values for x using the Table Input dialog box (2)In line y1 of the Graph Editor window, input and save y = 3x2 – (3)Tap 8. This displays the Table Input dialog box (4)Input the following values for the x-valuesof your table, and then tap [OK] uTo generate a number table by assigning list values to (1)Create and save the list of values to be assigned. list1 = 1, 2, 3, 4 Specify the list that contains the values you want to assign to •You can configure list data settings using the Graph Format dialog box •This generates the number table and displays the result on the Table window k Table Generation Precautions Editing Number Table Values Deleting, Inserting, and Adding Number Table Lines uTo delete a number table line (1) Tap the x-valueof the line you want to delete (2) Tap [T-Fact]and then [Delete] uTo insert a number table line uTo add a number table line Regenerating a Number Table Generating a Number Table and Using It to Draw a Graph Saving a Number Table to a List Generating a Summary Table uAutomatic x-valuesettings uUsing View Window xmin and xmax values as the x-valuesettings uSpecifying all x-values f(x) + f (x) – f (x) k Generating a Summary Table Using Automatically Set x-Values Page k Generating a Summary Table Using View Window Page k Generating a Summary Table by Specifying All of the Values for Making the Graph Editor Window the Active Window 3-5Modifying a Graph Page Page uTo modify multiple graphs simultaneously 9VbWaw Page kCycling Through Graph Changes Automatically 3-6Using the Sketch Menu uTo draw a line on the Graph window (1)While the Graph window is active, tap [Analysis], [Sketch], and then [Line] uTo write text on the Graph window (1)While the Graph window is active, tap [Analysis], [Sketch], and then [Text] •This displays a dialog box for inputting text uTo draw a line tangent to a graph Example: To draw a line tangent to the graph y = x2 – x – 2 when x (1)In line y1 of the Graph Editor window, input and save y = x2 – x – (2)Tap $to graph the function (3)Tap [Analysis], [Sketch], and then [Tangent] uTo graph the inverse of a function Example: To graph y = x2 – x – 2 and then overlay it with x = y2 – y – (3)Tap [Analysis], [Sketch], and then [Inverse] uTo draw a circle Example: To draw a circle with a center point located at (1, 1) and a radius of uTo draw a vertical or horizontal line Example: To draw a vertical line at x This displays a dialog box for specifying the •This closes the dialog box and draws the vertical line at x uTo clear figures inserted using the Sketch menu 3-7Using Trace (5)To quit the trace operation, tap on the icon panel kSpecifying the Format of the Coordinates Displayed by Trace Display coordinates and the Select the [Derivative/Slope] check box under derivative [Graph Format] Linking Trace to a Number Table Example: To link trace to a number table created by graphing y = 3logx xmin = –5 xmax = 5 ymin = –10 Generating Number Table Values from a Graph Page 3-8Analyzing a Function Used to Draw a Graph uTo obtain the root of a function Result Screenshots (2)On the Graph Editor window, input and store y = then tap $to graph it • Make sure that only y1 is checked 1x2 (x + 2)(x – 2) into line y1, and (3)Tap [Analysis], [G-Solve],and then [Min], or tap uTo obtain the point of intersection for two graphs uTo determine coordinates at a particular point on a graph To obtain the value of •This displays a dialog box for specifying the x-value (4)For this example, input 0.5 and then tap [OK] This moves the pointer to the location on the graph where uTo determine the definite integral for a particular domain ymin = –4 ymax = 4 (3)Tap [Analysis], [G-Solve],and then [ ∫ dx] •This displays “Lower” on the Graph window uTo determine the distance between any two points (2)Tap [Analysis], [G-Solve],and then [Distance] (3)Tap the first point on the Graph window •This causes a pointer to appear at the location where you tap (4)Tap the second point on the Graph window uTo obtain the volume of a solid of revolution (3)Tap [Analysis], [G-Solve],and then [ ∫ ( f(x))2dx] This displays a dialog box for inputting an interval of values for Using the Conics Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Using the 3D Graph Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Using the Sequence Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Using the Statistics Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Using the Geometry Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Using the Numeric Solver Application 9-1Numeric Solver Application Overview Clear all 1-characterinput variables (a through z) Clear a–z Initialize the upper boundary and lower boundary Initialize Bound Change the convergence range 9-2Using Numeric Solver (6) Tap 1, or tap [Solve] and then [Execute] on the Numeric Solver menu Example: Solve the equation 86 = 56.01205897 log(61− x) In this example, the initial convergence value is (2)k9 (3)Input the equation as written, then tap w Page Using the eActivity Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Using the Program Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Using the Spreadsheet Application 13-1Spreadsheet Application Overview 13-2Spreadsheet Application Menus and Buttons kGraph Menu kCalc Menu kSpreadsheet Toolbar Buttons Toggle the selected cell(s) between decimal (floating point) and exact display*1 Toggle the selected cell(s) between bold and normal M/ B 13-3Basic Spreadsheet Window Operations To have the cell cursor behave this way when you register input: Navigating Around the Spreadsheet Window kCursor Keys kJumping to a Cell Hiding or Displaying the Scrollbars Selecting Cells Using the Cell Viewer Window uTo view or hide the Cell Viewer window 13-4Editing Cell Contents Entering the Edit Mode kTapping a cell and then tapping the edit box To move the editing cursor here in the edit box text: Press this cursor key: kTapping a cell and then inputting something from the keypad Basic Data Input Steps Inputting a Formula uTo use the soft keyboards to input a function Page Inputting a Cell Reference kRelative Cell Reference kAbsolute Cell References This cell reference: Does this: uTo input a cell reference Inputting a Constant This input: Is interpreted as: And is treated as: Using the Fill Sequence Command uTo input a range of values using Fill Sequence Parameter Page Cut and Copy Paste kWhen the clipboard contains data from a single cell or the edit box If you do this: Executing the [Paste] command will do this: Page Specifying Text or Calculation as the Data Type for a Particular Cell When this data type is Inputting this into the cell: Causes this to be specified: Using Drag and Drop to Copy Cell Data within a Spreadsheet uTo drag and drop between cells within a spreadsheet kDragging and Dropping Multiple Cells uTo drag and drop within the edit box Using Drag and Drop to Obtain Spreadsheet Graph Data uTo use drag and drop to obtain the function of a graph uTo use drag and drop to obtain the data points of a graph Example: To obtain the data points of the bar graph shown below (1)Input data and draw a bar graph See “Other Graph Window Operations” on page Recalculating Spreadsheet Expressions Page 9bcdW0aE 9efgW0bE 9hijW0bE Importing and Exporting Variable Values kImporting data assigned to a variable into a spreadsheet uTo import the data assigned to an EXPR variable uTo import the data assigned to a LIST variable uTo import the data assigned to a MAT variable Example: To import the matrix data assigned to the MData variable at cell A1 (1) Tap cell A1 to select it (3)Type the variable name (in this case “MData”) into the [Variable] box kExporting Spreadsheet Data to a Variable uTo export spreadsheet data to an EXPR variable (2)On the [File] menu, tap [Export] •This displays the Export dialog box along with a soft keyboard •In this case, “EXPR” will be automatically selected in the [Type] box uTo export spreadsheet data to a MAT (Matrix) variable Searching for Data in a Spreadsheet kSearch Dialog Box Item Cell Contents Not Selected kSearch Examples Page Sorting Spreadsheet Data uTo sort spreadsheet data using the [Sort] menu command uTo sort using the sort toolbar button 13-5Using the Spreadsheet Application with the eActivity Application Page Page Page 13-6Statistical Calculations Enter the (2)On the menu bar, tap [Calc] and then [Two-Variable] kRegression Calculations uTo perform a regression calculation uTo paste a list of regression calculation results into a spreadsheet kDistribution Calculation uTo perform a distribution calculation Distribution Type Data uTo paste distribution calculation results into a spreadsheet 13-7Cell and List Calculations Page Page Cell Calculation and List Calculation Functions u Cell-Calculation- row u Cell-Calculation- col u Cell-Calculation- count u Cell-Calculation- cellif u List-Calculation- min u List-Calculation- max Page Page Page Page u List-Calculation- sum u List-Calculation- prod u List-Calculation- cuml u List-Calculation- Alist u List-Calculation- percent u List-Calculation- polyEval u List-Calculation- sequence u List-Calculation- sumSeq 13-8Formatting Cells and Data Text Alignment For this type of alignment: Number Format Changing the Width of a Column uTo change the width of a column using the stylus uTo change the width of a column using the Column Width command uTo change the width of a column using the AutoFit Selection command Page 13-9Graphing Page Page Page Page u[Graph] - [Bar] - [100% Stacked] ( ") u[Graph] - [Pie] ( Z) u[Graph] - [Scatter] ( X) u[Graph] - [Histogram] ( ) u[Graph] - [Box Whisker] ( ) Page u[Graph] - [Row Series] u[Graph] - [Column Series] Graph Window Menus and Toolbar k Edit Menu kType Menu Basic Graphing Steps Select this [Graph] menu option: Page Regression Graph Operations (Curve Fitting) uTo plot a scatter graph and then draw its regression graph (2)Tap [Graph] and then [Scatter] •This plots the scatter graph for the data you selected in step uTo show or hide lines and markers uTo change a line in a clustered line graph to a column graph uTo change a column in a clustered column graph to a line uTo find out the percentage of data for each pie graph section uTo change View Window settings uTo change the appearance of the axes uTo change the appearance of a graph by dragging a point Page Using the Differential Equation Graph Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Using the Financial Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Page Configuring System Settings 16-1System Setting Overview System Application Menus and Buttons Or select this System 16-2Managing Memory Usage Page Add-InApp. Tab eActivity Tab Language Tab This sheet lists language data used for the ClassPad menus and messages Shows the data for this language: 16-3Using the Reset Dialog Box 16-4Initializing Your ClassPad 16-5Specifying the Display Language 16-6Specifying the Font Set 16-7Specifying the Alphabetic Keyboard Arrangement 16-8Viewing Version Information 16-9Registering a User Name on a ClassPad 16-10Specifying the Complex Number Imaginary Unit 16-11Assigning Shift Mode Key Operations to Hard Keys Example : uUsing the Shift Mode with a Cursor Key Appendix 1 Character Code Table Page Page Page 2 System Variable Table an0 an1 an2 anE bnE bnE0 cn0 cn1 cn2 α-2-3 pˆ1 pˆ2 α-2-5 sx1 sx2 α-2-6 xy 3 Command and Function Index Page Page Page Page Page Page 4 Graph Types and Executable Functions Page y ◆ Page 5 Error Message Table Page Page Page kWarning Message Table Warning Message kLow Memory Error Processing This mark applies in EU countries only