The sample worksheets typically require some effort - they contain lost of
exercises (i.e. they are NOT ready made references).
They are targeted for teamwork since one person working alone too easily
gets stuck on elementary syntactical problems.
Save your own personal copies of the worked-out sample worksheets -- include lots of comments.
Once this library of sample worksheets is essentially complete, we recommend to download all files from the ftp-directory, and save all in the same directory on your own PC hard disk, floppy disk, or network drive. Then you may use the MAPLE hyperlinks to navigate between the sample worksheets.
1. File management, navigation; etc. (mostly MS-WINDOWS skills)
Know location and function of basic items on toolbars and pull-down
Expanding and collapsing sections on existing worksheets.
Move cursor to any point in worksheet. Select text/input/output by blocking it.
Use on-screen help to find information.
Recognize text, math input and math output regions.
Know the different roles between ENTER inside text and math-input regions.
Know the different roles of ENTER and SHIFT ENTER in each of text and math-input regions.
Copy (cut) and paste selected text/input/output into text or input regions.
Copy (cut), selected text/input/output and paste into other WINDOWS applications (e.g. MS WORD).
2. Worksheet formatting (MAPLE specific, similar in other computer algebra systems)
Advanced skill: (optional)
Work with hyperlinks: Define targets and links both inside and in between worksheets (only inside same network, no true URLs).
3. Exact arithmetic, algebra, and symbolic calculations
Factor polynomial expressions and expand products of polynomial expressions.
Understand the ambiguity of the word "simplify" in common usage.
Solve single equations in a single variable exactly when possible.
Understand that there are no higher order analogues of quadratic, cubic and quartic formulas.
Solve simple single equations in a single variable numerically.
Solve systems (SETS) of (typically linear) equations in several variables.
Familiarity with complex arithmetic in MAPLE.
Convert Root_Of format into decimal complex approximations.
4. Basic data structures, pure functions
Substitute expressions into each other (including substituting numerical values into expressions).
Understand the pure-function (arrow) notation.
Evaluate pure functions at symbolic and numerical inputs.
Compose pure functions.
New to release 5:
Insert a spreadsheet and use the FILL facility to create a table of function values.
Plot the data from the spreadsheet.
Convert e.g. lists into sets and vice versa.
Pick an element of an ordered list (know how to use both [.] and op).
5. Plotting (here essentially only single variable case)
Plot the graph of a pure function.
Plot a parameterized curve defined in terms of pure functions.
Customize plots using toolbars and plot options:
Know the contents of the plot-pulldown-menus and effects of the buttons on the toolbars.
Know about the HELP page for plot[options].
Be familiar what kinds of options are available.
Be able to use the plot options as needed (this list is fairly long!).
Recognize aliasing effects and take counter measures, e.g. by increasing the value of numpoints.
Know how to load the plots and plottools packages, and use HELP pages to learn how to employ the commands defined in these packages.
Animate sequences of plots (use display([...],...,insequence=true) rather than animate(...)).
6. Reading/writing data
Read (parse) a set of symbolic data (strings, mathematical expressions) from a text file into a MAPLE worksheet.
Write mathematical expressions to a text file from a MAPLE worksheet.
Save all current values of a MAPLE worksheet in form of an m-file.
Read all current values from an m-file into a MAPLE worksheet.
7. Calculus and the student package
Evaluate limits using MAPLE (effectively using L'Hopital's rule),
both at finite values and at infinity.
Calculate Taylor approximations.
Use the commands of the student package to visualize Riemann sums.
Use the commands of the student package to work with algebraic representations of Riemann sums.
New to release 5:
Use a spreadsheet to create a table for antiderivatives (indefinite integrals), or of derivatives.
Use numerical and graphical methods to check whether two analytic expressions may be algebraically equivalent.
Use numerical and graphical methods to reject obviously erroneous symbolic and numerical output.
8. Basic programming
Use for-loops to automate repeated calculations that differ only slightly.
Use the seq command to generate lists of numbers/expressions.
Use the map command to apply a pure function in parallel to all members of a list.
Use the op and nops command to access members of a single list or of nested lists.
Use proc to define multi-line procedures to automate more complex recurring calculations.
Declare local variables.
Understand the difference between local and global variables.
Programming in computer algebra systems provides completely new challenges, largely due to their ability to work with "unevaluated procedures and functions". If you are interested in more advanced uses of CAS please contact the author, or just visit the WWW-site of a recent (1998) class that targeted more advanced uses of CAS.