Finite Math for Windows PDF Manual - Weiss Software · 2006-06-28 · Finite Math for W indows xii Acknowledgments The developm ent of any large scale project such as Finite Math

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Finite Math for Windows Version 2

Howard J. Weiss

July 2006

Finite Math for Windows

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Table of Contents Chapter 1: Introduction Overview............................................................................1

Hardware and Software Requirements ..............................3 Installing the Software .......................................................4 The Program Group ...........................................................6 Starting the Program ..........................................................6 The Main Screen ................................................................7

Chapter 2: The Modules: A Sample Problem Introduction......................................................................14

Creating a New Problem..................................................15 The Data Screen ...............................................................17 Entering and Editing Data................................................18 The Solution Screen .........................................................21

Chapter 3: A Sample Calculator Introduction......................................................................23

Creating a New Problem..................................................23 Data Entry and Solution...................................................25

Chapter 4: The Main Menu File Menu .........................................................................28

Edit Menu.........................................................................34 View Menu.......................................................................36 Module Menu...................................................................36 Textbook Menu................................................................36 Format Menu....................................................................37 Tools Menu ......................................................................41 Window Menu..................................................................41 Help Menu........................................................................41

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Chapter 5: Printing The Print Setup Screen.....................................................46

Information to Print..........................................................47 Page Header Information .................................................48 Page Layout......................................................................48 Printer Options .................................................................50

Chapter 6: Graphs Introduction......................................................................51

File Saving .......................................................................54 Print..................................................................................54 Colors and Fonts ..............................................................55

Chapter 7: The Matrices Module Overview..........................................................................56

Creating or Loading Matrices ..........................................57 Operating on Matrices......................................................58

Chapter 8: Stepping Overview..........................................................................60 Linear Programming ........................................................60

Systems of Linear Equations............................................62 Matrices............................................................................65


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Preface

The goal in developing this software has been to provide students with a user-friendly Windows program in order to enable them to easily explore the topics commonly referred to as Finite Mathematics. While students have been successfully using calculators in order to obtain answers to Finite Mathematics problems, this software package provides much more capability than a calculator. $ Finite Math for Windows provides more models than a calculator. For

example, straight lines can be graphed based on any one of four forms (slope-intercept, point-slope, point-point, normal form) rather than the slope-intercept form required of calculators.

$ It enables students to see not only the answers but the intermediate calculations

for problems. For example, all of the computations involved in least squares, matrix multiplication, linear programming or systems of linear equations are shown rather than just the solution.

$ It will help students to decide what the next step is in a procedure. For

example, when solving simultaneous equations the student can choose the next step, have the computer perform the next step or have the computer show the student what the next step should be.

$ It can provide more or better visual displays for those topics that are graphical

in nature. For example, when graphing equations the parameters can be varied very easily using scrollbars in order to see the effects on the lines.

$ It provides more answers than does a calculator. For example, the student can

see a complete marginal analysis for linear programming with this software. $ The software comes with files for the examples in the most popular Finite

Mathematics textbooks including those by Armstrong & Davis; Barnett, Ziegler and Byleen; Goldstein, Schneider & Siegel; Lial, Greenwell & Ritchie, Maki & Thompson; and Mizrahi and Sullivan. This way the students can easily see how to apply the software to problems in the textbook.

This program has the standard look and feel of Windows so learning the package

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should pose no problem. Thus, with a small investment in time in exploring this exciting, new program, students will easily be able to completely solve problems in their finite mathematics textbook. Since it is a Windows program, students will have all the advantages of using a computer and Windows. That is, they can easily store, retrieve and print problems and solutions. It is possible to copy and paste between this program and other Windows programs - especially Excel. It is possible to format a table on the screen and then print the table as it is formatted. As with most Windows programs if you have more than one printer then it is possible to change printers. This includes printing to a fax! Most Windows programs today include an option to save as HTML. This program includes such an option. In addition, one of the exciting features in this package is the ability to save files as Excel files. This feature is available for nearly all of the modules. When it is used, the program creates an Excel file that contains not only the data but also either the formulas for the solution or a spreadsheet that is ready to be solved by using Excel’s Solver add-in. Finite Math for Windows has many features that allow the student to customize it to his or her own liking. For example, users may set options to have either the data shown or the solution shown when a file is opened. There is an option to automatically save the data after data entry is complete, an option to solve the problem after data entry is complete, an option to change the default titles for problems/data sets, several formatting/display options and several other options. The user support for this program is outstanding. It is possible to send e-mail messages directly to the developer for program help. Also, the software has a help option which points directly any software upgrades at the Finite Math Web site. Support of the package is offered through the web site http://weisssoftware.com/finitemath/and through

[email protected]

To the students who use this book, I hope you find that this software complements your text well. To the instructors who use this book, thank you for choosing Finite Math for Windows. I welcome your comments, especially by e-mail at [email protected].

http://weisssoftware.com/finitemath/


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Acknowledgments

The development of any large scale project such as Finite Math for Windows requires the assistance of many people. I have been very fortunate in gaining the support for my software and advice of students and colleagues from around the globe. Without their help, Finite Math for Windows would not have been developed. Discussions over the years with my colleague Fred Murphy have been very useful to me, especially in the area of mathematical programming. Leah Berman and Gordon Williams offered several very useful comments on a preliminary version of this software. There are several individuals to whom I must give special thanks. Rich Wohl, and Tom Tucker are the editors with whom I worked on my first software packages. Without the keen understanding that my editors had of computers, software, texts, students, and professors, the software development would still be a vision rather than a reality. Fellow authors have given me many useful suggestions. The support, encouragement, and help from all of these people are very much appreciated. As always, I must express my appreciation and love to my wife, Lucia, and my children, Lisa and Ernie, for their understanding and support during the many hours that I spent in front of my PC rather than with them. In addition, I am grateful for their valuable comments and suggestions regarding the look and feel of the software and I am indebted to Lisa and Ernie who have spent considerable time in testing the software for me.

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To My Family

Chapter 1: Introduction

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Chapter 1

Introduction Overview Welcome to Finite Math for Windows. This package is the first one of its kind and is a very user-friendly software package that has been designed to help you to better learn and understand Finite Mathematics. The software can be used either to solve problems or to check answers that have been derived by hand. Finite Math for Windows contains a large number of models that enable the student to solve or check solutions for a majority of the homework problems in Finite Mathematics textbooks. In this introduction and the chapters that follow, we describe the general features of the software. We encourage you to read these chapters while running the software on your computer. You will find that the software is extremely user-friendly due to the following features: Standardization $ The graphical user interface for the software is a standard Windows interface.

Anyone familiar with a standard spreadsheet, word processor, or presentation package in Windows will easily be able to use the software. This standard interface includes the customary menu, toolbar, status bar, and help files of Windows programs.

$ Even though the software contains 17 modules (11 models and 6 custom

calculators) the screens for every model are consistent, so that after you become accustomed to using one model you will have an easy time with the other models. Similarly, the screens for the calculators have the same consistent appearance which leads to ease of understanding and use of the calculators.

$ File storage and retrieval is simple. Files are opened and saved in the usual

Windows fashion and, in addition, file extensions are determined by module, which makes it easy to find previously saved files.


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$ Data and results, including graphs, can be copied and pasted between this application and other Windows applications.

Flexibility $ The screen components and the colors can be customized by the user. This can

be particularly effective on overhead data shows. $ The user can select the desired output to print and, in addition, several print

formatting options are available. $ The software can be set to automatically save a file after data has been entered

and/or to automatically solve a problem after data has been entered. User-oriented design $ The spreadsheet-type data editor makes data entry and editing extremely easy.

In addition, whenever data is to be entered, there is a clear instruction given on the screen describing what is to be entered. Also, when data is entered incorrectly a clear error message is displayed.

$ Intermediate steps in solving problems are generally available for display. $ The display has been color coded so that answers will appear in a different

color from data. $ There is a menu of modules available that corresponds to the textbook if you

are using a textbook on the list. User support $ Example files that correspond to examples from these textbooks are included

with the package. $ This manual is available from the HELP menu in two formats (DOC and PDF). $ Upgrades are available on the Internet through the download library, which

can be easily accessed. (http://weisssoftware.com/finitemath/). $ Help is available by contacting [email protected]. What all of this means to you is that with a minimal investment of time in learning the


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basics of Finite Math for Windows, you will have a very easy-to-use means for solving problems or for checking your homework. Rather than being limited to looking at the answers in the back of your textbook, you will be able to see the complete solutions or procedures for most problems. In many cases, the intermediate steps are displayed in order to help you check your work. In addition, you will have the capability to easily change the parameters on these problems or to solve bigger, more interesting problems. Hardware and Software Requirements Computer The software has minimal system requirements. It will run on any IBM PC compatible Pentium machine with at least 16 MB RAM and operating Windows 2000, Windows NT, Windows ME, or Windows XP. Monitor The software has no special monitor requirements. Different colors are used to portray different items. All messages, output, data, etc. will show up on any monitor. Regardless of the type of monitor that you are using, the software has the capability that allows you to customize colors and/or fonts and font sizes in the display to your liking. This is extremely useful for classroom displays. These options are explained in Chapter 4 in the section entitled Format Menu. Printer A printer is not required to run the software but, of course, if you want a hard copy (printout) then it is necessary to have a printer attached. The printing is standard so that no special features, characters, or printers are required. It also is possible to print to a file in order to import the printout into a word processor for further editing. Print options are described in Chapter 5.


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Typographic Conventions in this manual $ When we use boldface, we are indicating something that you type or press. $ When we use a bracket, [ ], we are naming a key on the keyboard or a

command button on the screen. For example [F1] means Function key F1, while [OK] means the >Okay= button on the screen.

$ We will use [Enter], [Return], or [Return/Enter] to mean the key on your

keyboard that has one of those names. The name of the key varies on different keyboards and some even have both keys.

$ We will use boldface and capitalize only the first letter to refer to a Windows

menu command. For example, File refers to the menu command. $ We will use all capitals to refer to a toolbar command such as SOLVE. Installing the software The software is installed in the manner that most programs designed for Windows are installed. For all Windows installations, including this one, it is best to be certain that no programs, including virus protection programs, are running while you are installing a new one. 1. Download and save the installation from

http://weissSoftware.com/finitemath/download.html or from Regnow.com. 2. Open the file and follow the setup instructions on the screen. Generally

speaking, it is simply necessary to click [NEXT] each time that the installation asks a question.

Default values have been assigned in the setup program, but you may change them if you wish. The default folder is C: \Program Files\FinMath. In addition to installing files into this directory please note that the software installs some files to the Windows System directory. The installation will back up any files that are replaced if you select the backup option (as you should). The setup program will ask you for registration information such as your name, university, professor, and course. All items are optional except for the student/user name that must be given. This name cannot be changed later! To change the other information from within Finite Math for Windows, use Help, User information. In the middle of the installation you will be given a choice of textbooks as shown

http://weisssoftware.com/finitemath/download.html


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below.

If you are using one of these textbooks then select this option. If you select one of those options the software will be customized for your text. This is very useful as the notation will match your text as will the menu order in the Textbook menu. To change the textbook registration use the Textbook menu item from the main menu or use Help, User Information. In addition, example files from the textbook will be installed. Looking at these example files while you are reading the text should make it perfectly clear to you how to use the software for that type of module. One option that the program will question you about is whether or not you want to be able to run the program by double clicking on the file name in My Computer or File Explorer. If you say yes then the program will associate the proper extensions with the program name. This is generally very useful. For example, if you double click on a file named >example.lin= then Finite Math for Windows will open and load the file. If you see a message saying that something is wrong during installation and you have the option of ignoring, then choose this option. The program will likely install properly anyway. The message usually indicates that you are running a program or have run a program that shares a file with this software package. Installing and Running on a Network With written permission it is permissible to install the software to a network only if the university has purchased a license for each student who will be using the software .


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The Program Group The installation program will add a program group with two options to the Start Menu.

. More importantly, the installation will place a shortcut to the program on the desktop.

The Finite Math for Windows icon is the option that may be used to begin the program. (The desktop icon is much easier.) Help is available from within the program, but if you want to read some information about the program without starting it first use the Finite Math for Windows Help icon. To uninstall the program use the usual Windows uninstall procedure (Start, Settings, Control Panel, Add/Remove Programs). The programs will be removed but the data files will not and will have to be deleted using My Computer or File Explorer if you wish to do so. After installing the program you should check http://weisssoftware.com/finitemath/support.html in order to determine if there have been any updates to the software that are posted. Starting the Program The easiest way to start the program is by double-clicking the program icon that is on the desktop. Alternatively, you may use the standard Windows means for starting the program. Click on Start, Programs, Finite Math for Windows, Finite Math for Windows in order to use the software. After starting the program, a splash screen will appear as shown below.


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Name The name of the licensee will appear in the display. This will be your name if you are running on a standalone computer or the network name if you are running on a network. The license expiration date will also appear if the software has been licensed through your university rather than purchased directly from http://weisssoftware.com/finitemath/download.html Version and Build Numbers One important piece of information is the version number of the software. In the example, the version is 2.0 and this manual has been designed around that number. While this is version 2.0 there is also more detailed information about the program version and that is the build number. The build refers to program updates. In this example the build is 12. The version and build can also be found using Help, About (displayed at the very end of chapter 4). If you send e-mail asking for technical support, you should include the build number with the e-mail. This will occur automatically if you send your email by using Help, E-Mail. The program will start a couple of seconds after the opening display appears. The Main Screen The second screen that appears is an empty main menu screen. The first time that this screen appears a Tip of the day form will appear as displayed below. If you don=t want the Tip of the day to show up each time then uncheck the box at the lower left of the form. If you change your mind later and want to see the Tip of the day then go to the Help menu.

http://weisssoftware.com/finitemath/download.html


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Also, please notice the background in the middle of the screen. This is referred to as a gradient. This gradient appears whenever the main screen is empty and it appears on other screens in the software. You may customize the display of the gradient by using Format, Colors as explained in Chapter 4. If you are seeing two colors rather than a gradient, then you most likely are not using your monitor to its fullest capability and might want to consider resetting your display properties by right-clicking on the desktop. After closing the Tip of the day, or if you have chosen not to see the tips, the next screen is the module selection screen. More will be mentioned about module selection in the next chapter. The menu will drop down automatically in order to lead you to what steps you need to take next.


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At this point, you should select one of the modules and begin your work anew. However, in order to display all of the screen components, we have selected a module and loaded a data file (shown on the next page). The top of the screen is the standard Windows title bar for the window. At the beginning the title is >Finite Math for Windows.= If you are using a text listed in the software and loaded the example files when the program was installed then the names of the authors of the texts should appear in this title bar at the beginning of the program. (If not, go to Textbook on the main menu.) The title bar will change to include the name of the file when a file is loaded or saved as you can see in the example. In addition, if it is a data screen, rather than a solution screen, then the word AData Table@ will appear in the title bar as shown below.


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On the left of the title bar is the standard Windows control box and on the right are the standard minimize, maximize and close buttons for the window-sizing options.

Below the title bar is a bar that contains the Main Menu. The menu bar is very conventional and should be easy to use. The details of the menu options of File, Edit, View, Module, Textbook, Format, Tools, Window, and Help are explained in Chapter 4. When there is no data the Edit option is not enabled, as there is no data to edit. The Window option is disabled when editing data since this option refers to results windows and we have no results until after we press the SOLVE tool. While the menu appears in the standard Windows position at the top of the screen, it can be moved if you like by clicking on the handle on the left and dragging the mouse.

Below the menu is a standard toolbar (also called a button bar or ribbon). This toolbar contains shortcuts for several of the most commonly used menu commands. If you move the mouse over the tool for about two seconds, an explanation of the tool (balloon help) will appear on the screen. As with most software packages, the toolbar can be hidden if you so choose (right click on any of the toolbars or use View,


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Toolbars, Customize). Hiding the toolbar, allows for more room on the screen for the data or solutions. As is the case with most Windows toolbars we allow the toolbar to float. In order to reposition any of the toolbars simply click on the handle on the left and drag. One very important tool on the standard toolbar is the SOLVE tool seen on the far right of the bar. This is what you press after you have entered the data and you are ready to solve the problem. Alternatively, you may use File, Solve or press the [F9] key. Please note that after pressing the SOLVE tool, this tool will change to an EDIT tool. This is how you go back and forth from entering data to viewing the solution. For some modules, there is one more command that is enabled on the standard toolbar. This is the STEP tool (second tool from the right in the toolbar), and it enables you to step through the iterations displaying one step at a time. STEP is available for Linear Programming, Systems of Linear Equations and Matrices. Chapter 8 in this manual details the use of this STEP option. Below the standard toolbar is a format toolbar. This toolbar is very similar to the toolbars found in Excel, Word and WordPerfect. It too can be customized, moved, hidden or floated.

There is one more toolbar and its default location is at the bottom of the screen. This bar is a utility bar and it contains five tools. The first tool is named PRINT SCREEN and it is there to print exactly what is on the screen. The next two tools, PREVIOUS FILE and NEXT FILE, will load files in alphabetical order either forward or backwards. This is very useful when reviewing a number of problems in one chapter. The two remaining tools allow files to be saved as Excel or HTML files. You may want to hide this toolbar in order to allow for more room on the screen for both the data and solutions. PRINT SCREEN and the two SAVE AS tools may be accessed from the File menu.

In the center are two areas, one of which is the main data table. The table contains a


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heading or title and then simply rows and columns. The number of rows and columns depends on the module, problem type, and specific problem. The large area with no grid is the table background. The caption colors, table colors and background color can be changed by using Format, Colors as explained in Chapter 4.

Above the data table is an area called the extra data bar for placing extra problem information. For example, in Linear Programming it is necessary to indicate whether to minimize or maximize. For least squares a value for x may be given in order to determine y. For Graph Theory, starting and ending node names may be given. These are all placed in the area above the data. If there is no extra data then an instruction panel fills the entire area above the data table. Otherwise, as shown above, on the right of the extra data panel is the instruction panel. There is always an instruction here trying to help you to determine what to do or what to enter. When data is to be entered into the data table, this instruction will explain what type of data (character, integer, real, positive, etc.) is to be entered. The instruction location can be changed by using the View option.

The data area also contains an area for annotating problems as shown on the annotated screen on page 10. A comment may be placed in here. When the file is saved, the information will be saved; when the file is loaded, the information will appear. There is an option when printing to print this. This comment can be dragged by grabbing it at the top between the pushpin icon and the eraser icon or the comment may have its window size changed. Also, clicking on the pushpin icon at the top left will close the display of the comment without erasing the comment. Clicking on the eraser will erase the comment and then close the box.

Towards the bottom of the screen is the status panel. The panel will display the module name as you select different modules. This is exemplified in this illustration where the title is >Linear Programming.=In the module for matrix operations, the bottom left panel in the status bar is used to display the computations for an individual


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entry in the matrix. The middle panel displays the type of screen. There are essentially three main screen types - data screen, solution screen and graph screen. For the most part, you go back and forth between entering data (the data screen) and viewing solutions (the solution screen). The graph screen is a special case of the solution screen. Graphs are discussed in Chapter 6. Finally, the names of the authors of your textbook are also shown in the status bar. The status bar can be hidden by using the View option. This panel can not be moved.


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Chapter 2

A Sample Model

Introduction

In this chapter we will run through a sample problem from beginning to end in order to demonstrate how to use the package. While not all problems or models are identical there is enough similarity that seeing one example will make it very easy to use any model in this software. In the next chapter we will demonstrate a sample calculator since these are somewhat different from the other models. As we mentioned in the introduction, the first instruction is to select Module from the main menu to begin the work. The list of modules will appear as shown below.

Alternatively, you may select the module by using the Textbook option from the Main menu (This is displayed in Chapter 4). As you can see, there are 17 modules available. 11 models are displayed above the line in the menu and 6 calculators are displayed below the line in the menu. The model and the calculators are separated in this menu because the look and feel of models differs from the look and feel of calculators. The calculators are demonstrated in Chapter 3.

Chapter 2: A Sample Model

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For the models there essentially is a simple six step process for doing the work.

1. Use File, New (or the toolbar icon) to begin a new problem. 2. Set the problem dimensions at the creation screen. 3. Enter the data on the data screen. 4. Use File, Save (or the toolbar icon) to save the problem. 5. Press SOLVE from the toolbar (or F9 or File, Solve) to get the answers. 6. Use File, Print to print the data and solutions.

When you are finished with the problem you may begin a new problem by restarting at step 1 with File, New. If the problem size of the new problem is the same as the old problem then you do not need to use File, New but may begin at Step 3 by simply entering the new data. There is one risk to beginning at Step 3 rather than Step 1. If you restart without File, New, then you must use File, Save As to save the new problem. If you use File, Save then it will overwrite your old problem. This is exactly the same thing that would happen in Word or Excel if you did not start with File, New. Creating a New Problem Generally, the first menu option that will be chosen is File, followed by either New to create a new data set or Open to load a previously saved data set. In the figure that follows we show the creation screen that is used when a new problem is started. In the case of the Critical Path Analysis and Graph Theory models you will first be given a choice of submodels before seeing the creation screen. Obviously, creating files is an option that will be chosen very often. The creation screens are similar for all modules but there are slight differences that you will see from module to module. One exception to the consistency of model creation is the Matrix module. Details about this model are explained in Chapter 7.


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The top line contains a text box into which the title of the problem can be entered. The default title for problems is initially >(untitled)=. The default title can be changed by pressing the [Modify Default Title] button. For example, if you change the default title to >Homework problem= then every time you start a new problem the title will appear as >Homework problem= and you would simply need to add the problem number to complete the title. If you want to change the title after creating the problem, this can easily be done by using the Format, Title option from the main menu bar or from the toolbar. For many modules it is necessary to enter the number of rows in the problem. Rows will have different names depending on the module. For example, in linear programming, rows are >constraints=, while in graphing lines, rows are >equations=. At any rate, the number of rows can be chosen with either the scroll bar or the text box. As is usually the case in Windows they are connected. As you move the scroll bar, the number in the text box changes; as you change the text, the scroll bar moves. In general, the maximum number of rows in any model is 90. There are three ways to add or delete rows or columns after the problem has been created. You may use the options in the Edit menu, you may use the tools on the toolbar, or you may right click on the data table and this will bring up both copy and insert/delete options. Two modules will have an extra option box, such as the one shown, for choosing the model type (Graphing Lines) or for choosing minimize or maximize (Linear Programming) or. Select one of these options. When you create a problem there is a tab control on the right. The first tab may be used to give default names to the rows and columns in the problem as shown above. Select one of the option buttons in order to indicate which style of default naming should be used. The row and column names are not used for computations. In most models the row names can be changed by editing the data table. The second tab contains a brief overview of the problem to help you get started as shown below.


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Some modules, such as, Linear programming or Systems of Linear Equations, require the number of columns. This is given in the same way as the number of rows. The program gives you a choice of default values for column names in the same fashion as row names. When you are satisfied with your choices, click on the [OK] button. At this point a blank data screen will appear as given in the following figure. Screens will differ module by module but in general, they will all resemble this screen below. As noted above, one exception to this is the screen for Matrices and this is described in Chapter 7. The Data Screen The data screen was described briefly in Chapter 1. It has a data table and for Linear Programming, Least Squares and Graph Theory there are extra data that appear to the left of the instruction, above the data table as shown previously in Chapter 1.


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Entering and Editing Data After a new data set has been created or an existing one has been loaded the data can be entered or edited. Every entry is in a row and column position. You navigate through the spreadsheet using the cursor movement keys (or the mouse). These keys function in a regular way with one very useful exception - the [Enter] key. The [Enter] key takes you to the next cell in the table, first moving to the right and then moving down. When a row is finished, the [Enter] key goes to the first cell in the next row that contains data rather than a row name. For example, in the screen above, if you are at the end of the row named >Equation 1' and you press [Enter] then the cursor will move to the cell with a >0' in the next row. It is possible to set the cursor to go to the first cell, the one with the name in it, by using Help, User information. In addition, if you use the [Enter] key to enter the data, after you are done with the last cell the program will automatically solve the problem (saving you the trouble of clicking on the SOLVE tool). This behavior can be adjusted by using Help, User information and in addition if you want the program to automatically prompt you to save the file when you are done entering data then this too can be accomplished


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through Help, User information. If an entry has a gray background, such as those in the right most column in the figure above, then it can not be changed. This will occur in the Graphing Lines, Graphing Linear Inequalities, Linear Programming and Systems of Linear Equalities models as exemplified below.

Notice that for these models (and also for Linear programming), you enter the variable names at the top of the column and only enter the coefficients in the table. The software builds the equation. For example, above we see that we have named the columns x, y and value and entered only the numerical coefficients for equation 1 and equation 2. The rightmost column is displaying the equation based on the column names and coefficients. The instruction frame on the screen will contain a brief instruction describing what is to be done. There are essentially three types of cells in the data table. One type of cell is a regular data cell into which you enter either a name or a number. When entering names and numbers, simply type the name or number; then press the [Enter] key or one of the direction keys or click on another cell. If you type an illegal character, a message box will be displayed indicating so. In general, it is possible to enter the data as either decimals or fractions. The section in Chapter 4 under the Format/Menu entitled Fraction/Decimal explains the use of fractions more fully. A second type of cell is one that cannot be changed. Not all cells that can not be changed have a gray background. A third type is a cell that contains a drop-down box. For example, the signs in a linear programming constraint or the signs when graphing linear inequalities are chosen from this type of box, as shown in the following illustration. To see all of the options, press the arrow on the dropdown box. You may select by clicking the sign with the mouse or you may type the corresponding key.


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If you right click on the data table then you will be presented with a menu of options as shown below.

You will be presented with the usual copy, insertion and deletion options and also with an option to save the table to an HTML file. When you are finished entering the data, press the SOLVE tool on the toolbar or use [F9] or File, Solve and a solution screen will appear as given in the following illustration.


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The Solution Screen

The original data is in black and the solution is in a color. Of course, these are only the default values as all colors may be set by using Format, Colors. An important thing to notice is that, for many models, there is more solution information available than only the one table displayed. This can be seen by the icons given at the bottom. Click on these to view the information. Alternatively, notice that the Window option in the main menu is now enabled as shown below the solution screen. The automatic dropping of the Window menu can be changed by using Help, User Information.


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The Window Menu

It is dropped down at the first solution display unless you reset this option by using Help, User information. Now that we have examined the creation and solution of a problem, we will demonstrate an example of the look and feel of the calculators.

Chapter 3: A Sample Calculator

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Chapter 3

A Sample Calculator

Introduction In Chapter 2 we displayed the list of modules available from the Module submenu on the main menu of the software. As we indicated before there are two general types of modules. In general, the type already displayed has data displayed in tables and multiple solutions. The calculator models typically have more submodels or options available than do the modules and in many cases require only limited data. Creating a New Problem When you select one of the calculator modules the calculator immediately appears on the screen. That is, calculators do not need dimensioning so you do not need to go File, New to begin a new problem. For example, if you select the Financial Calculator then the screen will appear as below.


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The calculators always appear as Tabbed Dialogs. An overview, similar to the one that is on the Creation Screen for the modules, appears on the rightmost tab for the calculators. Also, please notice that the instruction is on the calculator tab itself rather than in the area above the data as before. Four of the calculators have multiple models available as shown in the table below. Calculator Name

Models

Binomial and Normal Distribution

Binomial Normal

Counting Calculator

Additivity Principle Factorial Permutations Combinations Multiplications

Difference Equations

Finance Calculator

Simple Interest Compound Interest Annuity - Future Value Annuity - Present Value

Probability Simulator

Coin Toss Die Roll Sum of 2 Dice General Normal Distribution Binomial Distribution

Truth Table

These models are always displayed as option buttons on the left hand side of the calculator. In this example, the Financial Calculator has four models available that can be seen above. After selecting one of the models, in some cases the complete data screen will appear while in other cases you will be led through a step or series of steps to enter the data. For example, after selecting Compound Interest the calculator will appear as below.


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In this particular case, before being able to enter numerical data you are being asked to select which of five values should be computed (see the instruction). Also, at this point you may enter a title if you so desire. We show below the calculator after selecting the last option - compute the future amount after n periods. Data Entry and Solution


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At this point you enter the data into the first four text boxes in order to compute the value of the last item. In general, the Tab key will take you from box to box. The answer will be placed into the solution box as soon as all four entries are entered. That is, there is no need to press the SOLVE button. For example, after entering the 60 (months) in the place for the number of compounding periods the solution will be automatically computed as $1787.81 as shown in the screen below.

In the models exemplified in Chapter 2, the Window menu opened to display extra results. In the case of the calculators the extra results are on other tabs. For example, the Table tab contains the cash flow over time as partially shown below.


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As was the case with the other modules, the problem can be solved or printed by using the standard File options from the menu or toolbar. If you use File, New at this point, then the program will bring you back to the original Financial calculator. We now present a description of all menu options in Finite Math for Windows.


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Chapter 4

The Main Menu

In this chapter we explain each of the menu options. In general, these options are available for both modules and calculators. Where this is not the case, we will point that out. File Menu File contains the usual options that one finds in most Windows programs, as seen in the figure that follows.

These options are now described. New As demonstrated in the sample problem in Chapter 2, this option is chosen to begin a new problem/file. If you are in a model, rather than a calculator, then in most cases you will go directly to the problem creation screen. For the Critical Path Analysis and

Chapter 4: The Main Menu

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Graph theory models a pop-up menu will appear indicating the submodels that are available. After selecting a submodel you will go to the creation screen. For calculators, New will clear all data and bring you to the original calculator screen. Open This is used to open/load a previously saved file. File selection is the standard Windows common dialog type. An example of the screen for opening a file is shown below.

Notice that the extension for files in the software system is given as a function of the module name. The extensions are given in the table below.

Module Name

Exten-sion

Calculator Name

Exten-sion

Critical Path Analysis Games Graphing Lines Graphing Linear Inequalities Graphs Least Squares Linear Programming Markov Chains

PRO GAM GRA GLI NET LST LIN MAR

Binomial and Normal Dist. Counting Calculator Difference Equations Finance Calculator Probability Simulator Truth Table

PRB COU DIF FIN SML TRU


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Matrices Systems of Linear Equations Statistics

MTR SLE STA

For example, all graphing line files have the form *.gra. When you go to the open dialog, the default value is for the program to look for files of the type in this module. This can be changed at the bottom, where it says >Files of type=. If the files appear on your computer without the Agra@ extension it is because you have set an option in My Computer to AHide File Extensions for Known File Types@. This may be reset from My Computer or File Explorer if you want to see the Agra@. It is not necessary because the file type indicates that those files are for the Graphing Lines model. Otherwise, file opening and saving is quite normal. The drive or folder can be changed with the drive/folder drop-down box, a new directory may be created using the new button at the top, details about the files may be seen by using the details button at the top right.

It is possible to use Help, User information to set the program to automatically solve any problem when it gets loaded. This way, if you like, you can be looking at the solution screen whenever you load a problem rather than the data screen. Save Save will replace the current file without asking you if you care about overwriting the previous version of this file. If you try to save and have not previously named the file, you will be asked to name this file. Please note that only the data is saved rather than both the data and the solution. There is no need to save the solution since after saving the data the solution can be found simply by pressing SOLVE. If though, you want to save the data and solution, then this can be done by using the option of printing to a file rather than saving the file. The names that are legal are standard Windows file names. In addition to the file name, you may prefix the name with a drive letter (with its colon) or path designation. The software will automatically append an extension to the name that you use. As mentioned above, the extension is a function of the module name. You may type file names in as uppercase, lowercase, or mixed. Examples of legal file names are sample, sample.gra, c:myFile, c:\myCourse\test, and myproblem.example.


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If you enter sample.gra and the module is not graphing lines then an extension will be added. For example, if the module is Linear Programming then the name under which the file will be saved will be sample.gra.lin. Save as Save as will prompt you for a file name before saving. This option is very similar to the option to load a data file. When you choose this option, the Windows Common Dialog Box for Files will appear. It is essentially identical to the one previously shown. Save as Excel file Finite Math for Windows has an option that allows you to save nearly all of the problems as Excel files. The data is transported to Excel and the spreadsheet is filled with formulas for the solutions. In some cases, Excel=s Solver may be required in order to get the solution. For example, given below is the Finite Math for Windows display from a financial analysis model.

After saving as an Excel file, the Excel file appears below.


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Notice from the formula for cell B11 (shown in Excel=s formula bar) that a spreadsheet with formulas was created. That is, we did not >cut and paste= the Finite Math for Windows screen into Excel (which is also possible) but instead created an Excel spreadsheet with formulas to derive the answers. Save as HTML file Any individual table, either data or solution, may be saved as an HTML file as shown below where we have saved game results as an HTML file.


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If more than one table is on the screen at the time that this option is selected, then the active table is the one that is saved. We formatted the output table and then saved it as HTML. This, of course, looks much better in color. It is also possible to Save as HTML by right-clicking on any table. Print Print will display a Print Setup screen. Printing options are described in Chapter 5. Both Save and Print will act slightly differently if a graph is the active window at the time that you use Print or Save. Print Screen This will print the screen exactly as it appears. Printing the screen is more time consuming than a regular print. Solve There are several ways to solve a problem. Clicking on File, Solve is probably the least efficient way to solve the problem. The toolbar SOLVE icon is the easiest way or the [F9] key may be used. Also, if the data is entered in order (top to bottom, left to right, using the [Enter] key), the program will solve the problem automatically after the last cell. After solving, the Solve option will change to an Edit option on both the menu and the toolbar. This is the way to go back and forth between data and solutions. Note that Help, User information may be used to set the program to automatically maximize


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the solution windows if so desired. The Solve tool is not needed for calculators. Step For three modules (Linear Programming, Matrices and Systems of Linear Equations) a STEP button will be enabled to allow you to go through the solution process one step at a time. If you choose to step, the SOLVE button will change to FINISH and when you are done stepping you must select FINISH to get to the complete final results. Details and examples about stepping through problems are presented in Chapter 8. Exit The next option on the File menu is Exit. This will exit the program. Prior to exiting you will be asked to reconfirm the decision to exit. If you want to not be asked about this and simply to exit directly then reset the option using Help, User Information. Last Four Files The File menu contains a list of the last four files that you have used. Clicking on one of these will load that file. Edit Menu The commands under Edit can be seen in the following illustration. Their purposes are threefold. The first four commands are used to change the problem size. The second type of command is useful for repeating entries in a column, and the third type is for cutting and pasting between Windows applications. It is also possible to enable the insert/delete and copy options by right clicking on the data table and the copy commands may be invoked by right-clicking on any solution table.


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Insert row will insert a row after the current row and Insert column will insert a column after the current column. Delete row will delete the current row and Delete column will delete the current column. Copy Entry Down Column This command is used to copy an entry from one cell to all cells below it in the column. This is not often useful, but when it is, it can save a great deal of work. Copy Copy has four options available as shown below.

It is possible to copy the entire table, the current row, or the current column to the clipboard. It is possible to copy from the data table or any of the solution tables. Whatever is copied can then be pasted into this program or some other Windows program. Please note that the copy tool in the toolbar copies the entire table. If you are at the solution stage, the copying will be for the table that is active. The last option, Special, allows you to choose the number of decimal places to be copied. Paste Paste is used to paste in the current contents of the clipboard. When pasting into Finite Math for Windows, the pasting begins at the current cursor position. Thus, it is possible to copy a column to a different column beginning in a different row. This could be done to create a diagonal. It is not possible to paste into a solution table,


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although as indicated previously it is possible to copy from a solution table. It is very easy to copy and paste back and forth between Excel and Finite Math for Windows. View Menu View has several options that enable you to customize the appearance of the screen.

The Toolbars menu contains two options. The toolbar can be customized (as can most Windows toolbars) or the toolbar can be reset to its original look. The Instruction bar can be displayed at its default location in the extra data panel or above the data, or below the data, or as a floating window, or not at all. The Status Bar display can be toggled on or off. Full screen will toggle the display of all of the bars (toolbar, command bar, instruction and status bar) on or off. Zoom will generate a small form allowing you to reduce or increase the size of the columns in the tables. It is easier to use the ZOOM tool on the standard toolbar than to use the zoom menu option.. Module Menu A drop-down list with all of the modules will appear. The list is separated into two alphabetized sections. The top section contains what we have been referring to as model while the bottom section contains what we have been calling calculators. The separation is a reminder that the look and feel will be different between calculators and models as explained in Chapters 2 and 3. Textbook Menu In order to make it easier to use the software, we have created a second menu of module options. This second menu is ordered according to the specific textbook that


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you are using rather than in alphabetical order. We display an example of this menu for the Goldstein textbook below.

First notice that the textbook can be reset by using the Change Textbook menu item at the bottom of the menu. Then notice that the same modules appear that are in the Module menu but in this Textbook menu they are in order of the chapters of the textbook. Some chapters will have multiple modules, such as Chapter 1, and some modules will appear twice, such as Linear programming in both Chapters 3 and 4. Format Menu Format has several options for the display of data and solution tables, as can be seen in the following illustration. In addition, there are some additional format options available in the format toolbar. Most format options are disabled for the calculators since the calculators use textboxes rather than tables for data entry.


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Zeroes The first option allows you to decide whether or not zeroes should be displayed. In problems with a large number of zeroes it is usually a little easier to read the table if the zeroes are displayed as blanks. Fraction/Decimal Data may be entered as fractions in this program. It is possible to display the data, and in some cases the solutions, as either fractions or decimals. This needs some explanation though. If you enter data as 2 then you may display the data as either 2 or as .5 depending on whether you have chosen Fraction or Decimal from the menu (or toolbar). However, if you enter the data as a decimal, for example, as .5, then the program will display the decimal regardless of the choice you have made above. In other words, fractions will only be displayed if you have entered the data as fraction (and have chosen the Fraction display option rather than the Decimal display option.) Below we show an example with fractions displayed. In order for the fraction to be displayed it was necessary to enter the data as 5/2 and 17/2 rather than as 2.5 and 34/4; and it was necessary to select the fraction display (see the toolbar).

Max Decimals It is possible to limit the number of decimals that are displayed in tables using this drop down tool.


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Comma This determines whether large numbers should be displayed with or without a comma. For example, the display could be set to show 1234 or 1,234. Colors The colors for all of the displays can be set. There are five tabs as shown below. These options will create permanent changes whereas the foreground and background tools on the format bar will change only the current table. Furthermore, the color settings are for the entire table while the format tools may be used for either the entire table or for selected columns. The first tab is for setting the colors in the data table and the second tab is for setting the colors in the solution tables. That is, it is possible to have the displays of the data and the display of the results appear different, which can be helpful. For either the data or the results you may set the background and foreground colors for rows to alternate by using the odd and even options. This makes reading the tables easier.

In order to set the colors, first select the table property that you want to set, then select foreground or background if applicable, then select rows if applicable and then click on the color. For example, click on Body, Foreground, Odd and then click on the red color box and the foreground for every other row will become red. The changes here will be maintained throughout until you return to this screen and reset the colors. If you want to make changes in only one table for one problem then it may be easier to use the toolbar options for foreground and background. Also, the foreground and background color selection tools, as well as the bold, italic and underline tools may be used on individual columns if you select these columns before pressing on the tool.


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The third tab allows you to customize the colors in the panels (status, instruction). The fourth tab can be used to set the gradient that appears on several of the screens (problem creation, empty data screen) and the fifth tab allows you to reset the colors to their original (factory) settings. Other format options The font type, style and size for all tables can be set. The grid line display can be set to horizontal, vertical, both or none. There are four gridline styles available. The problem title that appears in the data table and was created at the creation screen can be changed. In order to give some idea of the extensive formatting capabilities available we display a sample of an overly formatted screen.

In order to create this screen we used Format, Colors and changed the background and foreground colors of odd rows to give us the alternating rows. After this we selected the column named >x1= and used the background, foreground and Bold tools on the toolbar to reset the colors and display for this column only. Then we selected >x2= and >x3= and used the Bold and Italic tools on the toolbar and finally we selected >x4= and used the center align tool on the toolbar. Expand and Squeeze Returning to the Format menu observe that the table can be squeezed or expanded. That is, the column widths can be decreased or increased. Each press of the tool changes the column widths by 10%. This is very useful when tables are wider than the screen. The toolbar has the zoom option which will accomplish the same thing. NOTE: All tables can have their column widths changed by clicking on the line separating the columns and dragging the column divider left or right!


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Tools Menu A Calculator is available for calculations. If Finite Math for Windows can find your Windows calculator then this will be loaded. Otherwise a small calculator will be loaded for doing simple calculations, including square root. Numbers may be copied from the calculator and pasted into an individual cell in the data table.

There is an area available to Annotate problems. If you want to write a note to yourself about the problem, select annotation. The note will be saved with the file if you save the file. An example of annotation appears in Chapter 1. In order to eliminate the annotation completely, the textbox must be blank. That is, the comment must be deleted/erased. If the file has been saved then it must be resaved in order to save the blank comment. Window Menu A sample of the Window options appears in the next illustration. This menu option is enabled only at the solution screen. Notice that in this example there are six different output screens that can be viewed. The number of windows depends on the specific module and problem.

Help Menu The Help options are displayed next.


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The first two options open up the Table of Contents and Index for the help file. The third option, Module Help, will give a description of the module, the data required for input, the output results, and the options available in the module. It is worthwhile to look at this screen at least one time in order to be certain that there are no unsuspected differences between your assumptions and the assumptions of the program. If there is anything to be warned about regarding the option, it will appear on the help screen as well as in this manual. Tip of the day The Tip of the day will be displayed. From this, it will be possible to set the tip to display all of the time or not to. E-mail This option will use your default e-mail program to set up a message to be sent to the software support email address. The first step is to click on the main body of the message and then to paste (CTRL-V or SHIFT-INS) the information that the program has created into the body of the mail. Before sending a message you may want to check to see if an upgrade has been posted in case you do not have the latest version. It is possible that the upgrade may have fixed your problem. The next two options point you to the Finite Math web site for general support of the software, including the location for the upgrade of this program.


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Manuals This manual is available as either a DOC file to be viewed using Word or any word processor that reads Word files or as a PDF file to be viewed using the Adobe Acrobat Reader (which can be downloaded from http://www.adobe.com/products/acrobat/readstep.html). User Information The first tab can be used to change the name of the course, instructor or school. The student name is set at the time of installation of the software and cannot be changed.

The second tab is used to set several of the options that have been discussed to this point.


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The third tab is used to set the associated textbook.. If you have a textbook on the list then you should use this option. There are very few differences when this option is set but one or two, in particular Markov Chains, are significant.

About Finite Math for Windows Notice the build number (build 12) after the version number. If you send e-mail requesting help please be sure to include this build number. Also, notice the web site location - http://www.weisssoftware.com/. This site will contain any upgrades. You

Chapter 5: Printing

45

should check this site for upgrades after you have installed the software.


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Chapter 5

Printing

The Print Setup Screen After selecting Print from the menu (or toolbar) the Print Setup screen will be displayed as shown in the accompanying illustration. There are several options on this screen which are divided over five tabs. The first tab is shown below. Before examining the tabs please notice that the bottom of the form contains three frames which if clicked will change the format between black/white and color; portrait and landscape; and ASCII and grid style printing.

Chapter 5: Printing

47

Information to Print The options in this frame depend on whether Print was selected from the data screen or from the solution screen. From the data screen, the only option that will appear is to print the data. However, from the solution screen there will be one option for each screen of solution values. For example, in the linear programming example above there are five different output displays as well as a graph available. You can select which of these get printed. In general, the data is printed when printing the output and therefore it is seldom necessary to print the data, meaning that all printing can be performed after solution. Remember, in general we have a six step procedure for approaching problems.

1. Use File, New to begin a new problem. 2. Set the problem dimensions at the creation screen. 3. Enter the data on the data screen. 4. Save the data 5. Press SOLVE to get the answers. 6. Use File, Print to print the data and solutions

Printing is the last step in this process. Printing Graphs If you select to print the graphs then the software will print the graph for that module. In the case of Critical Path Analysis, the results include two graphs -a Gantt chart and a precedence graph. If all you want is one of these two graphs, do your graph printing from the graph screen (described in the next chapter) rather than from a numerical output screen. Furthermore, if you want to control the size of the printed graph, use the options in the next chapter. Tables vs. Equations For the equation types of modules (Linear Programming, Graphing Lines, Graphing Linear Inequalities and Systems of Linear Equations), there is an option available about the style of printing. The problem can be printed in regular tabular form or in equation form. We show an example of each next.


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Tabular form Results ---------- x y RHS Dual Maximize 3 3 labor hours 3 4 <= 14 0.5 material (pounds) 6 4 <= 15 0.25 Equation form Results ---------- OPTIMIZE: 3x + 3y labor hours:+ 3x + 4y <= 14 material (pounds):+ 6x + 4y <= 15 Page Header Information The tab for the page header information is displayed below. There are six pieces of information that can be chosen to appear on the header. The first three options will appear on the first header line, and the second three will appear on the second header line. To make permanent changes to the course name or instructor name, use Help, User information.

Page Layout The tab for page layout is below. Please note that when the Print form is loaded Finite Math for Windows checks to see if it thinks you have a color printer by examining the name of the printer. If the name of the printer includes the word Acolor@ then the software expects you to choose to print in color while if Acolor@ is missing from the name then the software expects you to print in black/white. If your settings don=t match the software=s assessment of the type of printer that you have then a message will be displayed indicating as much. If you do not want this color check to occur then use Help, User Information to turn off the checking.

Chapter 5: Printing

49

Print as There are two styles of printing that may be used. The most common and fastest way to print is as ASCII (plain text). In addition, you may also print it as a grid similar to the one that appears on the screen. Thus, you may format the grid and then go to the print option and print a highly formatted grid. The formatted grids take longer to print than the plain text printing. Paper Orientation The paper can be printed in regular fashion (portrait) or it can be printed sideways (landscape). Answers Answers can be printed as bold, italic, color or any combination of the three. Do not look for color if you do not have a color printer. In fact, if you set the printing to use color on a black/white printer then the color answers generally appear lighter! This is usually not the desired characteristic. Margins The left, right, top and bottom margins can be set from zero to 1 inch in increments of .1 inches. The margin is above or beyond any natural margin that the printer itself has. Margins of zero allow for the most printing across the page. Maximum Column Widths The maximum widths of the columns (in characters) can be set. The leftmost column which


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is usually names can be set separately from the other columns. This is useful if you want to compress tables. Printer options The tab for the printer options appears below.

Print Timing Printing can occur each time that you use print or it can wait until the end, when everything will be printed at once. Printing each time is generally preferable but there are some situations where you want to wait until the end since this may save paper or minimize the number of trips to a network printer. Change Default Printer If you have more than one printer you may change the printer using this option. This changes the Windows default printer and may affect other programs! If you print as a grid then the printer selected is always the Windows default printer regardless of what you select. If Print to file is elected then the following option will be available. If the file already exists It is possible to print to the printer or to print to a file. If you print to a file you will be asked for a file name. Any name can be given. You also have the option of adding the printing to a file that was already there (appending) or erasing the file before printing (replace file).

Chapter 6: Graphs

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Chapter 6

Graphs

Introduction

Many of the modules have the capability to display graphs or charts as one of the output displays. There are several options that you have when a graph appears and in this chapter we explain those options.

When a graph is opened two or three things will occur. The graph will be displayed as a maximized window covering the entire area below the extra data. For some modules, a tab selector will be on the right of the graph (as shown above). Finally, two of the menu options, Print and Save, will change or execute differently. Notice


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that if the cursor is on over the graph then at the cursor a label is displayed which indicates the coordinates of the cursor. In this example the cursor is at x=1.1, y=1.5. Tab options For those models that include more than one equation or inequality the equation tab will appear as displayed above. The top half of the equation tab contains checkboxes for the equations or inequalities from the problem. Selecting the textbox will highlight the corresponding line on the graph. This can be very useful for determining the intersections of lines. For example, if you have several lines on a graph and check off two of them, those two lines will be displayed and you can easily see the intersection of the lines. If the model has only one equation then a different type of option will appear on the graph. For example, below we show the options available when graphing a single line. The coefficients for x and y or the constant on the right hand side may be changed and as you do so the line will move. Thus, with this software it is very easy and very interesting to see the effects of parameter changes on lines.

The second tab is named the Scale tab and can be used to easily manipulate the graph.

Chapter 6: Graphs

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In the figure that follows we show the Scale tab for the graph.

All graphs except for linear programming have the option to center the graph at coordinates 0,0. For example, if you look at the graph above you can see that it is not centered. Pressing the [Center at 0,0] button will rescale the axes so that the graph is centered. One other option is to display only the first quadrant by pressing the [Lower left at 0,0] button. The [Reset to Original] button will redraw the original graph in the event that you need to do so. Also, it is possible to rescale the axes by using the text boxes for the minimum and maximum values for the x and y axes. You must click the [Redraw] button after changing the values in the textboxes. Some graphs have grid lines by default while others do not as you can see from the graphs displayed above. However, for any of the graphs it is possible to control the grid lines by using the checkboxes to turn them on and off and the text box to space the grid lines. Finally, for the Linear Inequality and Linear Programming graphs it is possible to shade in either the points that satisfy the inequalities or constraints (the feasible region) or to shade out the points that do not by using the third tab named AFeasible@. Right-clicking If you right-click on any graph in the software then you will have the following menu displayed. The graph may be copied to the Windows clipboard for insertion in other Windows products, printed or saved as a BMP file.


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File Saving The file save option both under File on the main menu and on the toolbar will now save the (active) graph rather than saving the file. The file may still be saved by using File, Save as or by going to a results window other than the graph window. Print Print now will print the graph rather than presenting the general print setup screen. The print graph options are shown below. The graph can be printed in two sizes, and printed as either portrait (8.5 by 11) or landscape (11 by 8.5). Small graphs can be printed at the top or bottom of the page. Thus, there is slightly more customization of graph printing available through this method rather than when printing the graphs as part of the output as described in the last chapter.

Chapter 6: Graphs

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Colors & Font The foreground colors and the background colors may be changed by using the tools on the format toolbar. Changing the font name on the toolbar will change the font for the headings and labels in the graphs. Clicking on bold on the toolbar will change the font in the graphs to bold.


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Chapter 7

The Matrices Module

Overview The Matrices Module has a slightly different data display than do the other modules so it is worthwhile to look at it briefly. The first difference is that when selecting File, New, the creation screen has no options for sizing the problem. This is done on the data screen itself. After beginning a problem by selecting File, New, the data screen will appear as below.

Chapter 7: The Matrices Module

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Creating or Loading Matrices There is an area on the left that can hold one matrix (matrix A) and there is an area on the right that can hold a second matrix (matrix B). The extra data panel contains options for either dimensioning an empty matrix A or B or for loading a saved matrix A or B. For this example we will create a 2 by 3 matrix and a 3 by 4 matrix and multiply them. To create the first matrix press the [New A] button. This will change the area above the data to a dimensioning window as shown below.

Simply, select the number of rows and columns for the matrix. In addition, if you want an identity matrix then check the identity box at the lower left. After creating A and creating B our screen appears as below. At this point we simply enter the numbers for each of the two matrices. Notice that the middle of the Extra Data Bar contains a frame named AMatrix Operations@.


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Operating on Matrices After entering the data into the matrices we select the function from the drop down box in the middle in the area above the data. Our options are.

After selecting the function, press the SOLVE button (as usual) and the operation will take place and the solution will appear in a matrix below the data matrices as shown below. Please note that for Matrices the STEP button is also enabled. Stepping is discussed in more detail in the next chapter.

In addition, to a solution matrix, notice the statement in the lower left portion of the status bar. If you place the cursor over one of the cells in the solution matrix (Matrix

Chapter 7: The Matrices Module

59

C) then the computations used to create the cell will be displayed. For example, we have placed the cursor over the 60 in row 1, column 2 of Matrix C and this generates the display below.

The lower left area of the status bar contains the multiplications and additions used to compute the value 60. Also, Row 1 of Matrix A and Column 2 of Matrix B are highlighted (which is somewhat difficult to see in this manual). A second way to see the individual cell computations, is to use the STEP button rather than the SOLVE button from the toolbar. While it is possible to save the file in the normal, usual way, it also is possible to save any of the matrices. Saved matrices can then be loaded into matrix A or Matrix B. Thus, if you need to use the same matrix for more than one problem you could save the Matrix as well as saving the problem. Alternatively, if you need to use the output of one operation as input to the next operation then saving the solution matrix and loading it will work very well and easily.


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Chapter 8 Stepping

Overview Three of the modules have the capability to allow you to step through problems. The stepping operations are simple but since they vary depending on the module we will demonstrate them here. Please note that if all you want is to see the steps then you do not need to STEP through the problem. Instead, you may use SOLVE and then open the window that is titled Steps. The main advantage of the step button is that you have some control over the steps that are taken. That is, for example, you may decide which variable is the entering variable or you may decide on how to perform row operations on matrices. Linear Programming In the figure below we present a simple linear program.

Instead of using SOLVE from the toolbar we will use STEP. The window that appears is shown below. Notice that the table is titled ASimplex iteration 1".

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The software has set up a simplex tableau and is suggesting that the variable named AChairs@ should enter the basis. If you want a different variable to enter the basis then simply click on that column. After you have made your choice press on STEP again. The software will perform the pivot operations yielding the following table.

The software has pivoted on row 2 and is suggesting that ATables@ should enter the basis. Again, this may be changed if you like. In fact, you could work backwards by selecting Aslack 2" to enter the basis if you wanted to. When you are satisfied with the selection of the entering variable, press STEP again. This leads to the following screen.

Notice that the instruction indicates that we have arrived at the optimal solution. If we are satisfied (and we should be), then at this point click FINISH on the toolbar and this will lead to the final solution as though you had pressed SOLVE at the beginning rather than STEP. If you want to you may select a column and pivot again. This is


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useful for problems with multiple solutions. Systems of Linear Equations Below we show a simple system of two equations with two unknowns.

After pressing STEP, the screen appears as follows.

The problem appears in the table on the left and on the right there is a tab control for stepping. There are several options available that we will explain. First, it is possible for you to step or it is possible for you to have the computer do the work. If you decide to step, then the operations available in the frame titled AStudent@ are the three basic row operations. You may multiply a row by a constant, add a multiple of one row to another or exchange two rows. In this example we will choose to multiply a row by a constant. After clicking on the [Multiply a row by a constant] button the window appears as below.

The Step Details tab has opened and you need to change the multiplier to 1/3 in order

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to perform the work. After putting in 1/3 press the [GO] button on the tab. The new screen appears as shown below with row 1 updated.

Next you click on [Add multiple of one row to another] and put in the appropriate numbers as shown below.

After pressing [Go] the new table, with row 2 updated, appears as below.

If we let the computer continue then we have 3 options. If we click on [Step] the computer will perform the next step (multiply row 2 by 3/7). If we click on [Suggest] then the computer will show us the suggested next step. We demonstrate this below.


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Finally, if we press on [Solve] the computer will bring us to the final solution as shown below.

Notice that as was the case with Linear Programming, at this point we need to press FINISH to get to the complete final results as shown below.

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Matrices The matrix steps will have two different appearances depending on which operation is chosen. For inverses the appearance is very similar to Systems of Linear Equations while for adding, subtracting, etc the steps are shown but not in your control. Inverses Given below is a matrix that we wish to invert.


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After pressing step we get the same options as with Systems of Linear Equations.

The original matrix is in the first three columns and an identity matrix has been appended to the matrix. From here on out, stepping is as before. Other Matrix Operations For all other operations the display is the same. Consider the multiplication example below.

After pressing STEP we get the display below. In the answer matrix, only the first element is displayed. In addition, the row in matrix 1 and the column in matrix 2 that are used to perform the computations are highlighted (although the highlighting does not appear well in print). In addition, as is the case when you press SOLVE, if you put the mouse on top of the cell you will see the same computation in the status bar. As was the case before, after the last cell is computed you must hit FINISH to get the complete results.

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Documents

Finite Math for Windows PDF Manual - Weiss Software · 2006-06-28 · Finite Math for W indows xii Acknowledgments The developm ent of any large scale project such as Finite Math