MA 405 Complex Analysis Ashline

f(z) Special Edition

Copyright 1993, 1995 by Martin Lapidus, Lascaux Graphics

Installation instructions (Windows):

1. Create new folder called f(z) on your hard drive.

2. Drag f(z)sea from the disk accompanying your text Complex Variables with Applications (6th edition) by Churchill and Brown.

3. Double-click on f(z)sea. As a self-extracting archive, it will expand into the program file, mini-manual, and various examples.

4. Run the Special Edition by double clicking on the executable file F(z) in the f(z) folder.

5. To access information/updates about the Special Edition, look at Readme.txt in the f(z) folder. To access the thirty page mini-manual (excerpted from the User’s Manual for f(z)), look at Manxcrpt.pdf or Manxcrpt.txt in the same folder.

 

                    Installation instructions (DOS):

1.  Create a new directory called f(z) ( by typing md c:\f(z) ).

                              2.   Copy f(z)sea from the disk to that directory ( by typing copy a:*.*c: ).

3.  Double click on f(z)sea ( by typing f(z)sea ), which will expand into the appropriate files for this program.

4.  Run f(z) by typing f(z).

5.  To access information/updates and the mini-manual for the Special Edition, open Readme.txt and Manxcrpt.txt, respectively ( by typing edit readme.txt or manxcrpt.txt).

       

                      Running f(z):

        When you run f(z), your screen should look like the following:

 

 

 

 

 

 

 

 

 

 

 

When graphing complex functions with f(z), you should keep a few guidelines in mind:

  • At the beginning of an f(z) session, a domain and range window (denoted 1 and 2, respectively) will appear as well as a menu with 16 different command options. You can see these windows and this menu in the f(z) screen shown above. You can toggle between showing and hiding the menu on the right by clicking anywhere on your screen outside of the domain and range windows.

  • Note that each window has a tool bar at the bottom for moving the image in the window left, right, up, or down as well as zooming out or zooming in. There is also an option to view the image on the complex plane or the Riemann sphere (typically we’ll use the planar view rather than the spherical view).

  • In the bottom right of your screen should appear a small white box (it may have a question mark in it). After clicking on this box, a list of Keyboard Commands will appear and indicate shortcuts for various options that you can select in f(z). You can also access this Help panel by pressing the ? key on your keyboard. The type of Help screen to appear will depend on the part of the program from which you are seeking help.

  • On the real and imaginary axes of any complex plane in f(z), there are tickmarks at 1, i, – 1, and – i to help you estimate where points and graphs are located in the plane. To identify points more precisely in the plane, hold down the Alt key on your keyboard while moving the mouse pointer over the complex plane. The coordinates of the cursor position are shown in the lower left corner of the window. When done identifying points, release the Alt key.

  • In the menu appearing next to the domain and range windows, each command option can be selected either by clicking on it or by typing the letter that is capitalized in its name. Typically, after selecting one of these commands, a sub-menu will appear offering various sub-commands. A short description of each command (from the top to the bottom of the list) follows:

1.  Draw --- After specifying a complex function and a domain space (seen in one window), this command displays the image of the function in second window.

2.  deFine --- This allows you to specify for each window the function that will be graphed as well as the label for the window. There are other options which can be accessed here as well such as color or the type of view for the image. Possible views that can be selected include planar, spherical, 3d graph, or 4dgraph. We’ll make use of the planar option, although the other views are useful since each allows for a rotation of the image in the window.

Note: To graph the complex function w = g(z), you can select for the domain window the function F(z) = z [this is the default function for the first window] and for the range window the function F(z) =g(z) [the default function for the second window is exp(z)]. You will also need to make sure that the Operator for your functions is function (or composition) which you can select in the box under the function specification line. The default operator in your second window is composition which we’ll use most often; other operators available include addition, subtraction, multiplication, division, … , color by value.

3.  sCreen --- Using this command, you can change the type of resolution and aspect ratio for your domain and range. A higher aspect ratio horizontally stretches your images and a lower aspect ratio horizontally compresses them.

4.  domaiN --- This gives you the opportunity to select the domain format of your images. You can choose from such options as circles, lines, and points. The default format is 4 circles centered at the origin with maximal radius 2, 7 radii, 50 circular subdivisions, and 15 radial subdivisions. It should be noted that the more subdivisions are included in the domain, the longer it will take for the program to draw the graph of the complex function.

5.  Tools --- With this command, you can create a domain with your own specifications and see the image of your domain under your specified function. You can choose such figures as lines, circles, disks, points, and rectangles. You can also select the Pen option to draw any shape in the domain window and see its corresponding image in the range window. Once you’ve specified one domain and drawn its image, you can add more domain figures to see their images and remove such figures (either the most recent or all of them) using the rMv tool.

Note: This command is quite useful to determine the image of various domain regions (such as horizontal lines, vertical lines, or circles about the orgin) under a given complex function.

6.  Windows --- As the name suggests, you can create more windows with this command by clicking on Add Window in the Windows submenu. Each new window created is given a higher number (figure 1, then figure 2, then figure 3, and so on). To delete a particular window, simply click on it and click on Remove Window in the windows submenu. You may wish to open several windows to view the graphs of several complex functions simultaneously.

7.  Options --- With this command, you can modify various parameter increments for graphing. The default settings for these options should be fine for most of the work you will do in f(z).

8.  confiG --- With this, more graphing parameter changes can be made and, as with the Options command, the default settings for these parameters work fine for your use of f(z).

          9.  snapsHot --- This is disabled in the Special Edition of f(z).

10.  Animate --- This command can be used to create animation files. For each such file, you must specify a starting time, stopping time, and the number of frames to be animated. Several such animation files are included with the Special Edition of f(z). In your f(z) folder, all such files end in the extension .anm

11.  plaY --- Using this command, you can view animation files that have been created and are found in your f(z) folder. Examples of such animation files include mandzoom.anm (for zooming in on a Mandelbrot set) and loganim.anm (for viewing a complex logarithm).

12.  Save --- You can use this command periodically to make a copy of your work to a disk or the hard drive of your computer.. You will be prompted to give a file name (up to 8 characters in length) for your work. You should not put an extension on your file names since the extension .fz will be automatically appended to the name you choose. You can specify as part of the file name the drive or directory to which your file will be saved. If you don’t specify any such place, the default path and drive (listed above the box in which you will enter your file name) will be used.

13.  Load --- You can use this command to bring up a file which has been saved, either locally or on a disk.

14.  Print --- Using this command, you can make a hard copy of your work. A few items should be kept in mind when printing:

a.  Your output will look best when selecting as your default printer a Laser or Postscript printer.

b.  You should choose the "OK/ draw & print" option since the "print Now" option does NOT make any corrections in your output in terms of aspect ratio or color specifications.

c.  You can change the resolution of your output by increasing or decreasing the dpi (for example, increasing the dpi will sharpen your images at the expense of decreasing the size of the printed output).

d.  You can change the printer aspect ratio before printing (for example, increasing the ratio essentially "zooms in" on your images and stretches them horizontally).

15.  rEset --- This reinitializes all definitions and is useful if you wish to start over..

16.  Quit --- This will end your f(z) session.