"Interactive mathematics texts from Computer Algebra Systems:
use in teaching engineering students"

Dr. G. Keady and Dr N. Fowkes, University of Western Australia,
Dr J. Ward, Murdoch University

Engineering mathematics and its teaching

While CAS is useful to more people than engineers, we find that, as a group they are more receptive than some other groups. The explanation is probably as follows. In the following "engineers" also includes "engineering students".
  1. Engineers have sums to do, and a CAS can be a convenient "interactive reference source".
  2. Engineers are most motivated to use CAS when they are applied to problems which they see as relevant to their engineering interests, or which arise in their engineering courses.
  3. It appears most efficient to introduce a CAS when the students are sufficiently advanced in their courses to be moderately sophisticated in use of computers and in mathematics. Some programming skills - familiarity with if and for statements, etc. is useful. The students' mathematics needs to be sufficiently advanced that they are able to appreciate, understand and make real use of the CAS capabilities.
  4. A combination of a CAS and a traditional text seems to work better, for most students and teachers, than more radical efforts based entirely on Mathematica NoteBooks or Maple Worksheets.

PWS Notebook disks/electronic-supplements:
adding "interactivity" to PWS textbooks

Book publication of CA teaching materials is too slow and expensive. There have been many totally new texts, built ground-up after the packages: we do not think that these are, as yet, notably successful. Supplements to established texts are better. It is near impossible to keep printed materials - whole texts or supplements - up-to-date with current versions of the CAS. Electronic publication of notebooks is a much more efficient and cost-effective method of providing the support materials.

Starting from another point, there are huge numbers of Maple Worksheets and Mathematica Notebooks available. This leads to the question of how best to organise interactive text materials for students. There is no complete answer, but a partial solution, mentioned as (4) above, is to produce materials close to widely selling text-books. Some publishers, of which PWS is an example, are very supportive. PWS publish a series of inexpensive disks, "PWS Notebook disks". These are written to accompany existing texts they publish. So far these disks have been produced mostly for first year Calculus texts with large volumes of sales, including the books by Swokowski, and Dick and Paton. Neither of these texts are used in Perth, but they are used at various East Australian universities. There are other PWS Notebook disks associated with engineering texts not just engineering mathematics texts. PWS also runs a Web site.

The PWS Notebook disks' organization mirrors that of the texts, with chapter and section headings. Each section includes at least one fully worked example with problem solving hints, followed by ready-to-work exercises. A style guideline is available to PWS Notebook disk authors. An important restriction, needed to stop the tendency to add material, is to stay very close to the text. For first year texts this is rigorously enforced. In second-year engineering- mathematics texts, many results are merely presented, but not proved. Where the proofs are very short with a CAS it may be possible to include them in the electronic supplement. (The order of the truncation errors in the Runge-Kutta formula of S15.6 of Zill and Cullen is an example.) The requirement for notebook disks to stay close to the text means that there remains plenty of scope for individual lecturers using the text and its accompanying supplements to develop there own CAS applications which they may use as a focus of additional materials which reflect their special interests.

Maintenance of CAS materials, like the PWS electronic-supplements, as both text books and software move through different editions and versions requires workers. It makes sense, at least for the PWS texts which do not have first-year level volume sales, for at least some of these workers to be drawn from CAS- competent lecturers actually using the text in their classes.

For next year or so GK will be producing notebook materials to accompany Zill and Cullen "Advanced Engineering Mathematics" (PWS : 1992), a text in use at UWA and various East Australian universities. It is expected that PWS will be producing Notebook electronic supplements to accompany this text, there being a team of US CAS users to do this. Assuming GK's contributions are of sufficiently high quality, it is expected that they will be included in the PWS Notebook supplements. The other authors of this paper expect to check some of GK's efforts. The authors hope to convince the publishers that they should use the same team to produce similar supplements to accompany O'Neil "Advanced Engineering Mathematics" (in 1994 with Wadsworth - a sister company to PWS, and, now, 1995 in PWS), which is used at more Australian universities than is ZC. GK is specialising in the linear algebra and vector calculus parts (Part II of ZC), and the numerical methods parts (Part V of ZC). Many useful ideas can be salvaged from GK's Maple written earlier, separate from ZC, though much work remains to be done to achieve the uniformity of style required for the PWS supplement. GK's materials are available by anonymous ftp on 130.95.16.1 in subdirectories of /pub/keady. (Added Dec 95. Now also on the Web: click here.) (If a Notebook disk is produced, PWS will have rights to world sales for the disks accompanying the 2nd edition of ZC. The first version of GK's materials, for the first edition of ZC, will be available across the net, as this facilitates exchange between members of the team producing the PWS Notebook materials.)

Click here to go to the ACEC95 links page.