The Use Of Mathcad As A Lecture Aid For Compressible Flow

While Mathcad is primarily intended as a technical calculation and documentation aid, the use of this software for lectures in compressible flow was found to provide a number of advantages over traditional chalkboard approaches. For example, the students viewed much clearer and professional looking text, mathematics, figures and plots then would be possible using chalkboard based lecture and there was the additional bonus of the use of color. Handouts that duplicated the material presented were prepared and distributed thus giving students the opportunity to pay more attention to what was being said and less to copying notes from the blackboard. Lecture presentation was greatly facilitated by the Mathcad environment that made mathematical derivations simple through symbolic and arithmetical calculation, particularly those involving physical units. These same capabilities gave the instructor the ability to answer student "but what if...." questions during lectures by simply changing the calculation or derivation in real time and pursuing the line suggested by the student. As a bonus, it was easy to compile the lecture notes, examples, and quiz questions into an electronic book for the students to use in the future as the need to review compressible flow arises. While the time involved in preparing the initial set of lecture notes was much greater than the usual lecture preparation, the format that has been created will permit continuos future improvement with small additional expenditure of time. It may be possible in the future to further build on the electronic book as an aid or vehicle for distance learning. Introduction As is the case with most universities, Lamar University is experimenting with a number of alternate and multi-media mechanisms for the delivery or enhancement of education. All of these mechanisms involve substantial investment of capital resources at a time of constrained higher education funding. Therefore, the investments must be made in technology that has a direct educational pay off with very little room for failure. The ideal low risk path would involve an evolution of traditional instructional methodology into the emerging higher education environment of greater teaching obligations combined with students who may be time and/or location constrained. Mathcad appeared to offer some assistance along this evolutionary path at least for quantitative engineering courses. A project of using Mathcad to prepare and distribute lecture notes for a senior/first level graduate course in compressible flow was initiated. Since the lecture notes existed in electronic form, the next logical step of using other software packages to display these notes to students was also initiated. A simple hardware system consisting of a notebook computer (486DX20 with a 100 meg hard drive and Windows 3.1), an LCD color "Boxlight", and an overhead projector all mounted on a caster equipped table was scrounged. P ge 185.1 1996 ASEE Annual Conference Proceedings The initial lectures were presented using this hardware in conjunction with Powerpoint, a slide paradigm software package. Since the Powerpoint slides were prepared in Mathcad and pasted to the slides, digital storage quickly became a problem with a typical lecture requiring 10 megabytes. Therefore, it was decided to use Mathcad as the display software as well as the authoring software. This resulted in a loss of the slide paradigm, which was replaced by scrolling the Mathcad screen. An unexpected advantage was the retention of all the calculation tools previously available only during lecture preparation and not during the lecture. The topics covered in our compressible flow course consist of simple area change, normal shocks, simple friction, simple heat addition, combined change flow (analytic and numerical solutions), linearized 2-D supersonic flow, Prandtl-Meyer Flow, and oblique shocks. The outline of each topic generally followed the same format: a sketch of the system to be analyzed, a list of the assumptions, development of the constitutive relations, plots of these relations, and examples to emphasize particular physical behavior of the flow type of interest. Mathcad provides no means of making sketches so CorelDRAW was used for this purpose and imported to Mathcad. Previously, traditional lecture was used to verbally list assumptions and it was left to students understand their importance and copy them into their notes. A sketch and list of assumptions for simple heat addition (simple T 0 change) is shown below. Simple T0 Change (Rayleigh Flow ) ASSUMPTIONS : 1) steady flow 2) perfect gas ( P=ρ RT and cp and cv are constant) 3) no friction or other dissipative mechanisms 4) no mass injection or bleed 5) constant area 6) one-dimensional flow