2413labI1 - Laboratory I.1 An Introduction to DERIVE1 for...

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Unformatted text preview: Laboratory I.1 An Introduction to DERIVE1 for Windows The TAMUCC Mathematics Faculty This document is intended as a brief introduction to DERIVE, a program available to you on the TAMU-CC student (PC) network. DERIVE is capable of doing many routine calculations and graphs which will be helpful to you in calculus, and which you will use in your labs. Goals At the end of this lab the student will be able • to use Derive to author and manipulate expressions • to use Derive to solve equations, both algebraically and numerically • to use Derive to plot expressions • to know how to manipulate the plots, a little. • to save a Derive and submit it to the instructor. In The Lab NOTICE: In this document, ->this font<- refers to a menu item or title you will see on your screen in , and ->this font<- refers to an expression you need to type in, or an expression that tells you. In order to be able to use DERIVE on the network, you will first have to get a userid. You will get help doing this on the first day in lab. See any computer lab assistant for help at another time. . This will get you registered for a Novell Network account (Mac and PC) and a Kestrel Unix/internet account. We assume this is not your first exposure to Windows, and so we say nothing about the Windows interface. Using DERIVE’s Menus When you begin , you see the following menu titles, and a set of buttons underneath: File Edit Author Simplify Solve Calculus Options Window Help The above are the Algebra menus, one of two main menus for DERIVE. (The other main set of menus are the Plot menus. The Plot menus are covered later.) You will see below that it is necessary to use this menu (or the buttons below, or keyboard equivalent commands) for almost anything you do. This will be both a comfort and a curse. But that is the way works. What follows is an example of using in an elementary way. To save this document you are working on in DERIVE use File:Save (or ctrl-S, or alt-F:S, or the button with the floppy disk on it). (You will want to save your work from this and future 1 DERIVE is a registered trademark of SoftWarehouse, Inc., Honolulu, Hawaii 1 labs.) You can recall your work the next time you use by using File:Open (or ctrl-O, or altF:O, or the button with the file folder on it). The other option is to save your work on the disk space on your Novell account which can be accessed from any computer on campus that has access to the Novell network. Use the mouse to select the Author menu, then select Expression . . .. You will be prompted to enter an expression. Type 2+2 followed by the Enter key. Likely you will not be impressed with DERIVE’s response. Author:Expression simply recorded the expression you typed in and did absolutely nothing with it. Now select Simplify menu, then select Basic, followed by the Enter key. (I will quit reminding you to hit the Enter key from now on.) And (drum roll please) simplifies 2+2 to 4. This is the general rhythm you will have using Derive: first, enter an expression using Author:Expression, then do something do it (e.g., Simplify it). In Derive, there are usually multiple ways to get things done. For example, instead of selecting Author:Expression with the mouse, you could just hit F2, (ie, the F2 button on the top row of your keyboard) or alt-A:E, (ie, first press the Alt key and the A together, then press the E key) or push the button . ctrl-B, or alt-S:B, or the button , all get you Simplify:Basic. For the rest of today’s lab, we will introduce new commands and give their various ways to use them.; after today, we’ll just say “Author” or “Approximate” and let you do it anyway you want. Practice Authoring and Simplifying on the expression 1/2 + 1/3. Simplifying this expression results in a fraction. To get a decimal approximation, for it, use Simplify:Approximate (or ctrl-G, or alt-S:A, or the button ). Got the hang of it? Try entering the following expressions and see what the result of simplifying them is. Be sure to use Basic or Approximate simplification where necessary. > 2(7+8)/3^2 > sqrt(9) > ctrl-Q 9 > cos(0) > sin (ctrl-P) (note: typing ctrl-P is to get p) > cos(p/4) > 2^1/2 > (2^2)(1/2) > e^3 > #e^3 Since you will be turning in this DERIVE worksheet, now would be a good time to learn about textboxes. Textboxes are places for you to type plain text. You can start one by from the Insert menu by selecting Insert:Text Object (, or pressing F-2, or Alt-I:T, or pressing the button next to the Author button but has a pencil on it instead of math symbols). 2 Create a textbox and explain how you saw the difference between e^3 and #e^3. If necessary, go back and enter #e. Examples Using DERIVE Example 1: Solving an Equation Suppose you want to find the radius needed to have a circle of area exactly 10 square feet. Since 2 the area of a circle has formula A = pr , you need to solve this equation for r when A has the value 10. With DERIVE, this is a simple process. Author A = ctrl-P r^2. When you’re done hit Enter. You can check that the output is what you expected. Now choose Simplify:Variable Substitution (or ctrl-W, or alt-S:S:V, or the SUB button). The dialog box shows you the formula you typed in and a list of variables for that formula. If A isn’t highlighted in that list, click on it. Then if the cursor isn’t blinking in the Substitution box, click there. Type 10, the value you want to substitute for A, and hit Enter. Finally choose Solve:Expressions (or ctrl-shift-A, or alt-L:A, or the button of a hand lens showing and = sign). This will bring up a dialog box. Make sure that the variable r is highlighted, the method chosen is ‘algebraically’ and you don’t worry about the domain for now. Press the Solve button in the dialog box. (If you just press OK, you will have to Simplify the result. This alternative method shows, however, you can author a solve statement directly.) Regardless of you get DERIVE to solve the equation, there are two answers. The symbol between them is equivalent to the English word “or.” Which one is the radius of the circle you are seeking? How can you get a decimal value for the radius? Example 2: Graphing a Function x -5 . Author y = x-5/x+2. Look at the resulting x+2 expression. Is it what you intended? If not, you may have to retype it using parentheses. (By the way, you don’t have to do this, but if you’re a neat freak like us, you can get rid of an incorrect expressions by highlighting the expression and then pushing the Delete button.) † Suppose you wanted a graph of y = Once you have the right expression entered, and highlighted, you need to switch to the Plot window and menus. Choose Window:New 2D-plot Window (or ctrl-2, or alt-W:D, or the button). You should see axes, tick marks, and a new set of menus: File Edit Insert Set Options Window Help Now choose Insert:Plot! (or alt-P, or the button). x -5 As you should know, the function y = has a vertical asymptote at x = –2 and crosses the xx+2 axis at x = 5. If the plot you get doesn't contain these points, you need to enlarge the x and y † 3 scales of the graph. You can do this, as usual, in a multitude of ways: for now, either hit the F10 key or the button. Continue until you feel you have a good picture of the graph. To switch back to the Algebra window, choose Window:1 Algebra (or ctrl-1, or alt-W:1, or the button ). Example 3: Modifying Your Plot Suppose you want to focus on the point (5,0) in the above graph. If you went to the Algebra window, go back to the Plot window. The general idea on focusing on a point is, we move the cross you can see (probably near the point (1,1)) and then re-center the graph at the cross. Then zoom in. One way to move the cross is to use the mouse and click near the point (5, 0). Notice the bottom of your screen has the coordinates of the cross. If you didn’t get (5, 0) exactly, use the arrow keys to move back and forth until you do. (It’s possible Derive won’t let you get (5, 0) exactly, so get as close as you can.) Another way to move the cross is to use Set:Cross Position and then type in 5 for x and 0 for y. Now (5, 0) should be the point in the center of your screen. Finally, the goal was to “focus on” the point (5,0). Press F9, or the button. What happened to the scales for the x- and y-axes (the scales are on the bottom of the screen)? Press the F9 key several more times (you don’t have to wait for the graph to re-draw between the F9’s) until the scale is 0.1:0.1. Now, you should see a line that looks nearly straight. One point on that “line” is (0,5). Move the cursor to another point on the “line” with the mouse and record the coordinates. Now, you should be able to find the slope of the “line.” Make a textbox back in the algebra window and record the points and slope you calculated. Hint: You don’t need to use any other calculator other than DERIVE! Finally, back in the PLOT window, use the FILE:Embed command to paste a copy of the plot into the algebra window. If you are interested, you can copy the plot from DERIVE into the Windows clipboard for pasting into any other program as a .bmp image. Example 4: Tracing Your Plot As a brief final example, we want to show you how to use to trace out a plot. First, use the F10 key or the relevant arrow key to get a picture of the "whole" graph again. Then choose Options:Trace Mode (or alt-O:T, or hit F3). Now click somewhere on the screen. Note that immediately above/below your click, a little box appears on the graph. Use the left and right arrow keys to move the box back and forth. In the lower left hand corner of the screen, you'll see the x and y values changing as you move along the graph. At what x-value is the yvalue of the function closest to 3? What happens when you try to trace past the point of discontinuity? 4 In Conclusion You should now have some sense of how to enter expressions into DERIVE, how to plot them and how to manipulate the plot. If for some inconceivable reason you want to save the work you have done today, use File:Save (or ctrl-S, or alt-F:S, or the button with the floppy disk on it).(You will occasionally want to save your work from future labs.) You can recall your work the next time you use by using File:Open (or ctrl-O, or alt-F:O, or the button with the file folder on it). Saving a Derive file does not save your plots. If you want to save your plot, from 2D-plot Window, copy the graph into the Windows clipboard and then paste it into any other program such as Word and save this file in addition to your Derive file. Done? Choose File:Exit (no equivalents!) to leave. Ready for Lab? Usually there will be few questions that you need to answer before coming to lab. The report for the “Ready for the Lab?” part is due during the lecture time. Do not forget to use your book as a resource. After the Lab There will also be questions for you to answer about the work you have done in lab. Do not forget to go back and read the goals. These questions will be a great large part of your lab grade. There aren’t any After the Lab questions for this first lab. Be sure to save this document with all your notes about how you made DERIVE do what you wanted it to do. You will likely need to refer back to it in the future. Also, save a copy of the DERIVE file. If you don’t show it to your lab instructor as proof you did the work for this lab, you should find out how he/she wants you to turn it in. 5 ...
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