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Maple is a required tool for the science and engineering calculus/DE/linalg
sequence MAT 1500, 1505, 2500, 2705.
Mathematics is more than just arithmetic. It is about symbolic relationships between numbers and more complicated mathematical quantities based on numbers. Computer algebra systems (CAS) were designed as a tool for handling symbolic mathematical quantities and relations exactly, as well as in representing their numerical and graphical aspects, with mathematical word processing (verbal) later added as a bonus to weave all three of these aspects of mathematics (algebraic, numerical, graphical) together into a powerful platform for effective mathematical calculation and communication, backed up by an enormous amount of mathematical knowledge available to the intelligent user. Without understanding the mathematical concepts underlying its rich command structure, it is a useless tool—it does not substitute for learning the mathematical foundations, although it does free us from many routine and often pointless calculations, freeing us to give our attention to charting a path towards the solution of the real mathematical problems which confront us. It also gives us the opportunity to visualize many crucial ideas that can make dry mathematical notation come alive.
A computer algebra system (as opposed to other kinds of mathematical software) is the clear choice as the primary technology tool for aiding learning in a science/engineering based calculus, differential equations and linear algebra sequence, as well as in higher level mathematics courses (although more specialized tools are appropriate for advanced statistical applications). This is not to say that other choices of mathematical software are not also important in applications of this mathematics to science and engineering. Indeed Excel, MathCAD, and MatLab (all in use here at Villanova) all have important roles to play in various technical disciplines. Our choice of CAS is
Maple, perhaps the most widely used CAS in college education (together with Mathematica).
Goals in the Educational Process
Our goal in using Maple in this course sequence (1500, 1505, 2500, 2705) is not to teach
Maple for its own sake, but to use it as a tool in aiding your learning. Since some familiarity with a CAS is an important part of your background as a student in science and engineering in the 21st century, what you do learn about using
Maple can and should prove useful even after you complete these courses.
In order to be able to use Maple as a tool to aid learning, it is important to get familiar with the most useful aspects of its worksheet interface which a little Windows environment savvy and exploration easily accomplishes. Any mathematical activity that is not able to be addressed by intuitively building standard mathematical expressions and referring to a few help tips should be guided with a template from your instructor or a textbook technology supplement. By asking your instructor when necessary, and referring to
Maple help and MLRC help personnel when necessary, whatever difficulty you have in using
Maple can be overcome. There is no need to be frustrated. Work with a partner, and if you get stuck, get help but do not waste time.
Fortunately starting with
Standard
Maple 10, a reliable extremely useful set of palettes and context dependent right-click menus have been introduced which enable a new user who knows no
Maple syntax to do almost all the calculations needed for the calculus, differential equations and linear algebra sequence courses in which it is a required tool. Within Standard
Maple, the Tools Menu, Tutors submenu combines these features into an even more powerful popup applet window for many basic concepts that allows parameters for the activity to be set in the window, delivering a final result to the worksheet, but allowing mouse selection, Control C copying, and Control V pasting of extra window content into text regions of the worksheet as well. Feedback from
Maple helps unblock a student who does not see how to choose the next step in a multi-step Tutor activity. Similarly the Tools Menu, Tasks, Browse option allows you to browse the Calculus list of typical activities that are provided with worksheet examples that may be easily inserted into your worksheet where you need them.
[For new user startup information about Classic
Maple worksheets in 1d math input mode, see
Classic Maple Resources. The beginning of the Standard
Maple worksheet cmdlist1.mw described below summarizes how to start using that interface.]
While outside projects using Maple can enhance your ability to use Maple and show you how it can help you solve much more interesting and realistic problems, it is important to use
Maple in selected homework problems from your textbook on a regular basis so that it can help you in learning the concepts. In order to be effective, these problems should be chosen carefully keeping in mind the goal of enhancing your learning of the concepts, although it is also useful to do some routine problems to get familiar with using certain commands to substitute for the "back of the book" odd answer key as a check on your hand calculations.
Our 1500-1505-2500 Calculus sequence
Textbook by Stewart has its accompanying CalcLabs with
Maple, Single Variable manual which discusses Classic Maple. The first two chapters can be read and the input lines typed in within about an hour or less, depending on the individual. This is one way to start getting acquainted with
Maple. Proceeding along in this book then builds on this knowledge. However, by using Standard
Maple, most of this is unnecessary. By adapting examples in auxiliary Maple
calculus manuals or occasionally in the textbook from the 1d math Classic input mode in which they are typed one character after another to the new 2d math
Standard input mode (rather easy since one can literally type them into the 2d math input regions character for character if desired, while using 2d input features when desired within these expressions), they can still be helpful.
Calculus, Differential Equations and Linear Algebra Sequence
Command List Worksheets
The following worksheets explore most of the pedagogical tools Maple has available for performing routine mathematical calculations and visualizing concepts appropriate for elementary applications in the course content. They may be consulted by instructors or interested students alike,
although in practice few of either seem to have extra time to browse these
supplementary resources.
These hyperlinked worksheets can be opened directly by clicking on their
links in Internet Explorer or Firebird if you have a network or local copy of
Maple through the file association with the file extension .mw or .mws [some
math faculty offices and in UNIT public sites, some computer classrooms]. If you are using
citrix delivered Maple, the file association is broken, and you have to first save the files from these web links and use
Maple to open them [using Standard Maple to open the .mw files, or Classic Maple
to open the older .mws worksheet files]. However, it is much more efficient
to copy the hyperlink shortcut of a Maple worksheet and then within the Maple
program use the File Menu, Open URL command to paste in that URL and then open
it directly from its web location.
These certainly provide a good starting place for instructors to familiarize themselves with the tools
Maple has for teaching this course sequence, where supporting use of Maple is required by the syllabus.
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