Symbolic / graphical programs.

Symbolic algebra programs, such as Mathematica, Matlab, Maple, Mathcad and others offer the possibility of a substantially altered mode of undergraduate physics instruction, emphasizing realistic problems, graphic presentation and greater student involvement. The mode of utilization may depend on context (class size, frequency of meeting, instructor experience and degree of interactivity).

MAPLE, MathCad, Mathematica.

Students find Maple substantially easier to use than Mathematica; they find the Mathcad interface easier than either. For students (e.g. biological science majors and pre-medical students) who may not do much subsequent analytical and numerical class work, Mathcad might provide an easier interface if the introductory physics course is considered in isolation. Maple might still be preferable if used also for introductory calculus, chemistry etc., or because of greater available of adaptable Maple material. For an integrated sequence of science based courses, standardization on a particular platform offers obvious advantages.

The degree of Maple programming skill required of students can be progressive, possibly starting with simple worksheets allowing change of parameters and output plotting (modeling). It is relatively easy to design worksheets which require a minimal number of commands. The number of commands can be gradually increased over the term.

Maple's strengths include solving equations, making graphs and animations, doing calculus operations, vector operations, matrix manipulation,etc.The operations can be done either numerically or symbolically and it is often useful pedagogically to do both. Although a large application it can be used very effectively with present desktop and laptop computers even when doing complicated graphs and animations..Generally it is unsuited to deal with large numbers of objects like interacting bodies; if used for complex calculations for a large numbers of data points it will consume large amounts on time.

Evolution vs. Revolution

In time, packages like Maple may revolutionize the way physics courses are taught, making swift work of some topics now covered at length, and eliminating the need for others entirely. At present, however, we are at the point of looking for opportunities to insert Maple use at various places in conventional physics courses. Sometimes this use of Maple may be no better than by-hand work, but often it will be better, due to display, or animation, or dispensing with complex functions by integrating directly. As time goes on and we will develop more uses for Maple, and a major shift in emphasis and content may occur.

Classroom Use of Maple

The heart of a physics course is 'doing the physics' - sizing up the problem, identifying the principles involved, and preparing to solve the problem. Students should actively participate in this process during class, and when the setup is complete, the instructor can give the instructions to Maplefor obtaining a solution. Class participation is important either in predicting a range of expected answers before the solution, or by evaluating (sanity-checking) the solution found by Maple. This should be reinforced on exams by giving most of the credit for discussion of the setup and for sanity-checking the answer, and much smaller credit for the answer itself.

If students in an introductory physics course see flawless Mapledone in class, they are likely to be discouraged when they sit down to work with Maple on their own . But if a few mistakes are made in setting up and executing a solution in Maple during class, students will have a more realistic and forgiving attitude toward their own Maplemistakes.

Maplecan also be effectively used in class as a demonstration, often in the form of an animation, to show some particular physical behavior. MAPLE might also be used to generate a graph or set of graphs, to stimulate class activity ( 'What does this graph tell us about the two objects at t=0?' , 'Which of the graphs of electric field and electric potential go together?', etc.) It is also an easy way to examine limiting conditions.

Maple 'Labs'

In intermediate or advanced physics courses, it can be a really good idea to give up one lecture for a 2-hour lab session as the occasion arises. Students and instructor then work together to solve a problem, create an animation, etc. in Maple. This is especially important where students may be new to Mapleor rusty in using it. There is a different relation between instructor and students in this setting, which is likely to be valuable to both.

Maple Homework and Sample Worksheets.

In every course it is probably desirable to provide students with some sample Maple worksheets.

'Canned' worksheets may be fine if the instructor only wants students to explore the effect of changing parameters on a graph or a numerical value. This will not build Maple skills, but in certain courses playing with parameters may be important, while skill-building is not.

If the object is to have the student develop Maple skills, the sample worksheet will illustrate certain commands or functions, but will be structurally quite different than the homework assignment, so that students cannot just change a few values and turn it in as completed homework.

Worksheets containing a lot of discussion and sparse Maple code are likely to be more effective than worksheets with dense Maple code and only a few remarks.