Texas Instruments Derive 5 Introduction Manual
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Texas Instruments Derive 5 Introduction Manual

Texas Instruments Derive 5 Introduction Manual

Ti derive 5 calculator software: user guide
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T I
E X P L O R A T I O N S
™
by Bernhard Kutzler
& Vlasta Kokol-Voljc
S O F T W A R E
™

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  • Page 1 E X P L O R A T I O N S Introduction to ™ by Bernhard Kutzler & Vlasta Kokol-Voljc S O F T W A R E ™...
  • Page 2 Bernhard KUTZLER Vlasta KOKOL-VOLJC Introduction to ERIVE The following Derive™ 5 documentation is being provided as a courtesy of the authors, Bernhard Kutzler / Vlasta Kokol and the publisher Texas Instruments. We invite you to use the following abbreviated document during your personal evaluation of Derive™...
  • Page 3 Kutzler, Bernhard & Kokol-Voljc, Vlasta Introduction to D ERIVE 2000 2000 Kutzler & Kokol-Voljc OEG, Austria 1. Edition, 1. Printing: March 2000 Typesetting: Bernhard Kutzler, Leonding, Austria Cover art: Texas Instruments Incorporated, Dallas, Texas, USA The author and publisher make no warranty of any kind, expressed or implied, with regard to the documentation contained in this book.

  • Page 4: Table Of Contents

    Table of Contents Introduction ... 1 Chapter 1: First Steps ... 3 Chapter 2: Documenting Polynomial Zero Finding ... 23 Chapter 3: The Whole and Its Parts – Subexpressions ... 43 Chapter 4: Equations and Inequalities ... 63 Chapter 5: Approximate Versus Exact Computations ... 83 Chapter 6: Sequences and Families of Curves ...
  • Page 5 Preface The desire to make D 5 easily and quickly accessible led to this book. ERIVE Many thanks to Albert Rich and Theresa Shelby, the principal authors of D 5, for their ERIVE continuous support during the writing of this book. Many thanks to Patricia Littlefield and David Stoutemyer who polished the language of this book.
  • Page 6 Introduction is a mathematical computer program. It processes algebraic variables, expressions, ERIVE equations, functions, vectors, and matrices like a scientific calculator processes floating point numbers. D can perform numeric and symbolic computations, algebra, trigonometry, ERIVE calculus, and plot graphs in 2 and 3 dimensions. The main strength of D algebra and powerful graphics.
  • Page 7 By solving typical mathematical high school level problems, you will learn to handle D much as necessary for everyday use and for teaching or learning mathematics. You will learn how to use the major commands, keys, and functions. At the end of each chapter you will find a summary of the features learned in that chapter.

  • Page 8: Chapter 1: First Steps

    Chapter 1: First Steps makes it easy to perform mathematical operations: Enter an expression, apply a ERIVE command, and a new expression is obtained. All expressions can be used for new computations—just like on a piece of paper. This chapter teaches the basic techniques of using 5.
  • Page 9 Chapter 1: First Steps Work with D by entering expressions and applying commands, thus creating a worksheet. ERIVE After starting D , the system is ready to accept user input via the Expression Entry Toolbar, ERIVE as is indicated by the blinking cursor in the toolbar’s entry field. Input mode can be implemented with the Command Toolbar’s tenth button from the left, labeled  Learn more about the button by moving the mouse pointer onto it.
  • Page 10 Kutzler & Kokol-Voljc: Introduction to D Replace the last input by  Enter 1/2+1&3 (¢). When a syntax error is detected, the cursor is moved to the location of the error and the cause of the error is displayed in the Status Bar’s first pane. In the above example D unexpected special character.
  • Page 11 Chapter 1: First Steps  Simplify using This is different from what an “ordinary” calculator would produce. A mathematician once asked: “How do you recognize a mathematician?” and suggested the following answer: “A mathematician considers expression #5 a beautiful result.” Most students strive to replace such an expression by the corresponding floating point approximation.
  • Page 12 Kutzler & Kokol-Voljc: Introduction to D worksheet. Other objects (including text objects) are added after the highlighted object. To insert a text object above the square root of 24, first highlight the object that is now above it.  Highlight expression #3.  Display a function description of the onto it.
  • Page 13  Approximate using The answer is displayed in scientific notation. Since the count of whole digits is one more than the power of 10, the number has 173+1 = 174 digits. In the next exercise, you will learn a different technique of entering expressions by using the buttons preceding the entry field.
  • Page 14 Kutzler & Kokol-Voljc: Introduction to D ERIVE This button produced two expressions, #13 and #14 and has the same effect as entering the unsimplified expression with (¢) or , then simplifying it with . It is, therefore, a convenient shortcut for the frequently used “enter and simplify.” This example also shows how convenient fast input is in D .
  • Page 15 When correcting the most recent input, you can take advantage of the fact that a copy of the most recent input and the focus are still in the entry line.  To edit the expression use the right arrow key (Æ) to remove the highlighting. Change the input to 2/(x+1) by adding the parentheses, then enter the expression with (¢).
  • Page 16 Kutzler & Kokol-Voljc: Introduction to D  Edit the input string to 4x-1/(x-5) then press (¢). When working with D , focus can be either in the entry line or in the algebra window (View). ERIVE When focus is in the entry line, (Esc) will move focus into the View. When focus is in the View, button or its hot key equivalent, (F2), moves it into the entry line.
  • Page 17 Chapter 1: First Steps The last two examples are remarkable for two reasons. First, they demonstrate the importance of using parentheses to differentiate between (meaning ) and (meaning ). Second, expression #20 shows how carefully D simplifies expressions. ERIVE The third power of is entered as follows:  Enter ( -1)^3.
  • Page 18 Kutzler & Kokol-Voljc: Introduction to D  . . . then invoke the command by clicking on it with the left mouse button. opens the Expand Expression ERIVE commands that require specification of parameters. The above dialog box requires the specification of the expansion variable and the amount of expansion.
  • Page 19 This is another “beautiful” result. Before computing an approximation, add an appropriate comment to the worksheet in form of a text object.  Insert a text object with the The following is an approximation of sin(pi/4)  (Try to) conclude the input with (¢). The ‘Enter’...
  • Page 20 Kutzler & Kokol-Voljc: Introduction to D In D you can specify virtually any precision, meaning number of significant digits used for ERIVE arithmetic. The practical limitations are given by the available memory and your patience. Note that computing time increases with increasing precision. Update your text to indicate the chosen precision.
  • Page 21 Chapter 1: First Steps  Prepare for changing the font size: Open the Font Size field’s dropdown selection menu by clicking on  Select the number 10. Alternatively, you could make the Font Size field active, then overwrite 12 with 10. Now, announce the next example with an appropriate text.
  • Page 22 Kutzler & Kokol-Voljc: Introduction to D The text object is selected now as is indicated by the frame around it. Make sure there is no cursor inside it. If there is, press (Esc) again.  Delete the empty text object using the (Del) key.  Insert a new text object after the highlighted expression #26 (using the text “Next we.”...
  • Page 23  Change the font size to 10 points by scrolling within the then selecting the number 10, or by overwriting 12 with 10 via the keyboard.  Close the dialog with (_OK_). When continuing to write into the text object you started (you may need to click into the text object to put it into text editing mode), it still is in 12 point size, because the setting you just changed effects new text objects only.
  • Page 24 Kutzler & Kokol-Voljc: Introduction to D ERIVE  Select the Options>Display menu’s first choice (i.e. Alignment of New Objects This invokes a dialog box that allows you to control the alignment of all the objects that can be in a D worksheet.
  • Page 25  Carry out the change by leaving the dialog box with (_OK_). This font is useful for demonstration purposes, especially when using an overhead projector with a display palette. For personal work the small font may be preferable. Therefore, switch back to it and try a different color instead.
  • Page 26 Kutzler & Kokol-Voljc: Introduction to D ERIVE There are also three methods for entering the base of the natural logarithm e. Use all three of them to enter a sum of three e’s, then add the ordinary letter e to see the difference between a variable with this name and the famous constant.
  • Page 27 Summary Algebra Window or (Del) ... delete highlighted expression or (F5) ... insert text object after the highlighted object Insert>Text Object or (F2) ... enter expression, move focus into entry line Author>Expression Simplify>Basic ... simplify highlighted expression Simplify>Approximate File>Exit ... exit D ...

  • Page 28: Chapter 2: Documenting Polynomial Zero Finding

    Chapter 2: Documenting Polynomial Zero Finding The emphasis in this chapter is on creating a simple mathematical document about the finding of the zeros of a polynomial. At the same time you will learn the corresponding basic techniques of using D ERIVE  Start D ERIVE...
  • Page 29  Enter the above polynomial by preparing for expression input with y=x^4/2+3x^3/4-5x^2-7x/4-1/2 (Intentionally leave out the /4 in the middle term.) the key (¢) or the button (_OK_) will be displayed only in ambiguous situations. From here It will not be used any more for simple inputs such as the above. It is important for some of the features you are going to study and use in this chapter that you work with the above polynomial.
  • Page 30 Kutzler & Kokol-Voljc: Introduction to D ERIVE  Prepare for plotting a 2D graph: Open a 2D-plot window by clicking on the 2D-plot Window button or selecting the Window>New 2D plot Window command. created a plot window, so that you now have two windows to work with: an algebra ERIVE window and a 2D-plot window.
  • Page 31 that of the algebra window. In particular, the Status Bar displays the following graphics information: gives the coordinates of a movable cross, Cross Center gives the coordinates of the picture center, Scale gives the scale factors of both axes, The crossed square icon preceding the word  Draw the graph using the Oops—the Plot Expression...
  • Page 32 Kutzler & Kokol-Voljc: Introduction to D ERIVE Now the Plot Expression button is available, and you are ready to plot the polynomial.  Draw the polynomial’s graph using the Plot Expression button Now we have both an algebraic and a graphical representation of the polynomial available. However, the graphical representation is outside the algebra window’s worksheet in its own independent plot window.
  • Page 33 The color of the cross can be changed using the When the plot window is active, the cross can be repositioned by either moving the mouse pointer and clicking the left mouse button or by using the arrow keys (Æ), (æ), (½), and (¼).  Move the mouse pointer to (1,-1), or near it, then click with the left mouse button to move the cross to this position (left picture).
  • Page 34 Kutzler & Kokol-Voljc: Introduction to D ERIVE  Turn trace mode on by selecting the Trace Plots command. When trace mode is switched on, the cross changes its shape into a square and jumps vertically to the curve, with its horizontal coordinate unchanged. The expression number of the traced curve is displayed in the plot window’s Title Bar (here: Tracing Expression #1 ).
  • Page 35 The plot window “follows” the square. This means that the plot ranges for the horizontal and the vertical axes are changed automatically to ensure that the cross is visible. Since this mode can destroy a chosen plot range, follow mode should be used carefully and is therefore switched off by default.
  • Page 36 Kutzler & Kokol-Voljc: Introduction to D not found a position at which the y-coordinate is zero, but you can say that the polynomial zero must be between 1.6 and 1.62, probably being closer to 1.62. An obvious approach for getting closer is magnification.
  • Page 37 When you don’t like the change of the aspect ratio such is in the above pictures, you can easily restore it. You will learn how to do this in Chapter 4. Insert a text object documenting the method and result of your findings.  Insert a new text object and enter the following text (use the numbers you found):  Search for more zeros: Make the plot window active, then move the square to the uncertain middle section.
  • Page 38 Kutzler & Kokol-Voljc: Introduction to D Move the square to get a better approximation of the left zero.  Move the square near the left zero and note the cross coordinates in the Status Bar. Now the change of sign happens between x=-0.62 and x=-0.618. Produce a graph with steeper intersections to get a more accurate answer.
  • Page 39 Chapter 2: Documenting Polynomial Zero Finding  See what happens if you confirm with (_OK_). Notice the complicated numbers below the tick marks (your numbers are likely to be different) and in the Status Bar scale factors. This is caused by the graphical box selection.  Zoom in again using the Set range with box button...
  • Page 40 Kutzler & Kokol-Voljc: Introduction to D  Use the trace mode square to find approximations of the two zeros. The left zero lies between -0.6181818 and -0.6174242; and the other zero probably is at -0.5. All the above work now should be documented in the algebra window’s worksheet by embedding the graph and adding an appropriate text object.
  • Page 41  Enter the text: “Next we compute the polynomial’s zeros by applying the SOLVE function to the corresponding polynomial equation.” Generate the corresponding polynomial equation.  Highlight the polynomial #1, move focus into the entry line with (F2) (which is the hot key for authoring expressions), then auto-paste a copy of the polynomial using the hot key (F3).
  • Page 42 Kutzler & Kokol-Voljc: Introduction to D  Enter the text “Expression #4 gives the four exact zeros of the polynomial.” In order to compare these results with what you found graphically, approximate expression #4. Before doing so, again add a textual description of your approach.  Enter the text “We approximate #4 so that we can compare it with what we found graphically.”...
  • Page 43 Chapter 2: Documenting Polynomial Zero Finding Before sending a document to the printer, it is a good idea to do a print preview.  Look at the print preview using the File>Print Preview command. Print preview offers various options including a button for zooming in.  Zoom in with (_Zoom_In_).
  • Page 44 Kutzler & Kokol-Voljc: Introduction to D Make the expressions slightly larger. Change the expression font size via the submenu.  Prepare for changing the expression font size: Close the print preview window with (_Close_), then select the command Here you can select the expression font size, choose between the printing of Annotation s and...
  • Page 45 Chapter 2: Documenting Polynomial Zero Finding  Prepare for printing the document using print preview’s (_Print_) button. Make sure that the printer is properly connected, switched on, and set. In the Printing dialog box you can change the printer or the printing properties, change the print range from to either a range of pages or the highlighted expressions, or change the number of copies from the default 1 to the number you want.
  • Page 46 Kutzler & Kokol-Voljc: Introduction to D ERIVE Saving the worksheet preserves your work for later use or modification.  Save the worksheet by selecting the File>Save As command. suggests storing the file in the subdirectory Math . You may choose a different directory ERIVE by selecting one from the selection menu that is offered for the Save in...
  • Page 47 Summary Algebra Window or (Ctrl)+(ª)+(E) ... solve equation Solve>Expression ... open 2D-plot window or switch to one ... right justify highlighted object ... center highlighted object File>Save As ... save worksheet using a name File>Print Preview ... print preview or double-click left or right of expr..edit highlighted expression Edit>Derive Object Options>Display>Cross ...
  • Page 48 Index ... 124 ... 35 ... 35 5x – 6 = 2x + 15 ... 63 ... 117 cos( ... 125, 132 ... 67, 75 ... 75 ° ... 147 ... 137, 138 := ... 66, 96, 138, 167 ... 138 ...
  • Page 49 annotation of expression ... 6 annotation’s position ... 106 apostrophe ... 51 Apply parameters to rest of plot list applying differentiation ... 207 Approximate button ... 6 approximate computations ... 230 approximate mode ... 83 approximate step by step ... 88 approximation tools ...
  • Page 50 Kutzler & Kokol-Voljc: Introduction to D colon-equals ... 66, 96 color ... 98 Color by ... 125 Command Toolbar ... 3 commands ... 12 common denominator ... 60 complex branch ... 230 Complex factorization ... 60 complex plotting mode ... 231 complex-valued function ...
  • Page 51 drag text field ... 107 ... 216 DSOLVE e ... 21 edges of triangle ... 194 Edit ... 122 edit D text ... 15 ERIVE Edit>Copy ... 54, 201 ... 201 Edit>Copy Plot Window Edit>Cut ... 54, 201 Edit>Delete ... 60 Edit>Delete All Annotations Edit>Delete All Plots ...
  • Page 52 Kutzler & Kokol-Voljc: Introduction to D follow mode ... 30 font ... 105 font color ... 20 ... 16 Font Size Formatting Toolbar ... 15, 37, 85, 113, 243 Fortran File ... 201 four-function calculator ... 136 function as ordered pairs ... 169 function definition ...
  • Page 53 inverse function ... 226, 233 isolated points ... 194, 228 ... 257 ITERATE ... 257 ITERATES jagged ... 131 JPEG File ... 201 label number ... 4 labeled box ... 117 labels ... 4, 195, 224 least squares fit ... 159 length of vector ...

  • Page 54: Chapter 10: Parametric Plots

    Kutzler & Kokol-Voljc: Introduction to D Options>Display>Font of New Text Options>Display>Grids ... 115 Options>Display>Plot Color Options>Display>Points ... 99, 155, 194 ... 29 Options>Follow Cross Options>Hide Labels ... 224 Options>Plot Real and Imaginary P Options>Printing>Expression Layout Options>Printing>Header and Footer Options>Renumber Expression Options>Simplify Before Plotting Options>Startup ...

  • Page 55: Index

    real numbers ... 142 Real radio button ... 92 rectangular part of the screen ... 201 recursive functions ... 256 remove highlighting ... 10 rendering program ... 139 replace a subexpression ... 50 replace expression’s variables ... 49 replace old expression with new one ... 24 reposition annotation ...
  • Page 56 Kutzler & Kokol-Voljc: Introduction to D Solve>System ... 71, 159, 190 sphere ... 236 spherical plot ... 236 spiral staircase ... 177 square brackets ... 72, 137 square root ... 5, 11 Start menu ... 3 Starting Value ... 109 Status Bar ...
  • Page 57 variable ordering ... 47, 67 Variable Substitution button ... 156 VECT ... 157 VECT ... 95, 160, 210 VECTOR Vector dimension ... 153 vertical length ... 101 vertical scroll bar ... 85 View ... 3, 11 visualize ... 93, 117, 155 window type ...
  • Page 58 Texas Instruments U.S.A. 7800 Banner Drive Dallas, Texas 75251 ti-cares@ti.com ©2000 Texas Instrumentso www.ti.com/calc DERIVE/OM/1L3/A...

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