Senior Elective Gets Boost from Mathcad

Notre Dame uses Mathcad as the centerpiece for computations in a new Chemical Engineering course

"Mathcad makes it simple to generate solutions to mathematical models and present graphics in a convenient and easy-to-use fashion - it's a vital component of the course."

In 1995, Professor Roger Schmitz had an idea to develop an elective course for Chemical Engineering called "Topics on Ecology and the Environment." He felt that these topics could be taught from a chemical engineering perspective and that they would add nicely to the experiences of students in this program of study.

He wanted this senior-level course to focus strongly on mathematical modeling and simulations. After evaluating a number of software packages, Professor Schmitz chose Mathcad and found that it was an enormously useful product for a variety of tasks. "I was looking for something that was easy to use, something quick for students to learn, something with the tools and functionality to serve as the centrepiece of calculations for the course. I chose Mathcad."

In 1999, the course became a reality and now, after four years, students do 90% of assigned work for the course using Mathcad. They present their Mathcad worksheets in class or in group sessions and submit them electronically as homework assignments. Professor Schmitz says that Mathcad is ideally suited for such presentations: "Students see all their equations and calculations in standard math format and, because it's live, they can demonstrate the effects of parameter changes on the spot. It's immediate."

"Among our projects is a simulation of the carbon cycle aimed at addressing such environmental questions as, 'What levels of atmospheric CO2 might be reached over the next century?' and, 'What is the possible effect of those levels on the earth's temperature?' Other topics relate to the mechanisms of ozone formation and destruction in the stratosphere and the dynamics of various models of food webs and ecosystems. In all instances, the mathematical models comprise a system of nonlinear differential equations. Simulations involve numerical solutions, which are readily obtained with Mathcad. Spreadsheets are simply not suited for the task."

Another aspect of Mathcad that appeals to Professor Schmitz is the fact that he spends almost no time in the classroom teaching his students how to use the software. "I give them a brief introduction along with several example Mathcad worksheets to get them started. Then, they learn on their own by hands-on use in their assigned work. They seem to enjoy learning about the software and putting it to use. Since every topic covered in the course incorporates Mathcad worksheets - in simulations, examples, assignments - they get a lot of exposure to the program."

As a more than 40-year veteran of chemical engineering education, Professor Schmitz remains active in the Chemical Education community. He recently published a journal article in Chemical Engineering Education on the carbon cycle that references the Mathcad simulations used in the Topics course. In fact, he's hoping that the materials he has prepared for this course eventually evolve into an E-book. Meanwhile, he provides a CD containing all of the course material to his students. "As it stands, presently, the CD contains a PowerPoint slide show with links to course materials including Mathcad worksheets, spreadsheets of source data, and virtual experiments using LabView."