Reproduced with permission from NeXT Computer, Inc., USA, NeXT on Campus, Fall 1990. ã 1990 NeXT Computer, Inc., USA

University of Iowa 
First-year calculus meets the real world 
  
The University of Iowa has run calculus labs since the early 1970s.  In the 1980s, the math department implemented a special accelerated calculus section in which students cover the content of three semesters in two.
 
"We wanted to revise our accelerated calculus curriculum to present calculus as the language of science and show students real-world applications.  We needed for 
up-to-date scientific computing as part of that revision," says Keith Stroyan, professor of mathematics at the University of Iowa.  After a comprehensive review of hardware and software, Stroyan decided on the NeXT Computer and Mathematica.
 
"NeXT offers Macintosh-like ease of use and Mathematica software with the `notebook' front end, but runs a UNIX network and has a host of bundled software besides Mathematica," explains Stroyan.
 
Stroyan felt the NeXT Computer's built-in networking capabilities would make it easier to manage course files. "NeXT runs on a genuine Ethernet network.  Also, NeXT delivers low overhead in terms of system programmer maintenance, and it looked like other UNIX workstations were going to be pretty high maintenance.  Our network of 12 NeXT computers almost ran itself last semester." 
 
Last year marked the introduction of the school's revised accelerated calculus class using the NeXT and Mathematica. "It was a radical departure," says Stroyan.  "For 
example, in the first week of class, we talk about epidemic models, which is really a system of differential equations." 
 
Before advanced computers were available, an instructor would never have thought of mentioning differential equations on the first day of calculus.  But the theories behind an epidemic model and how to interpret one really are not that difficult.  "The students don't have enough calculus to solve the differential equations, and this is where the computer takes over for us.  Mathematica can solve the approximate equations and it draws graphs at the same time, so the students can see what the model predicts without struggling through the differential equations."  Students understand even more as they fill out the shell notebooks that Stroyan and his teaching assistants prepared. 
 
The student notebooks are an integral part of this calculus curriculum, and the NeXT Computer's large, high-resolution display makes the notebooks easier and more useful to work with than Stroyan had anticipated.  "When I first got the NeXT Computer, I thought, `oh no, I really made a mistake.'  Then I worked on it for a few days to get some notebooks together.  When I went back to my Mac, it seemed like a toy.  That's because the NeXT has higher screen resolution and is about four times the size of a Mac color screen.  With the NeXT you can lay out two big notebooks side by side, compare them, and go back and forth.  For doing this kind of work, the big, high-resolution screen is important."
  
The NeXT Computer has enabled Stroyan to teach in ways that weren't possible before.  "The three-dimensional graphics are spectacular," he says.  "It's hard to plot graphs of surfaces.  Traditionally, we have only been able to plot simple, special-case equations.  Now we can study and graph multivariable calculus in the first year.  We also spend a lot of time studying dynamical systems, and there we make animations, or flows, that show how the solutions to these equations change in time.  That's something you can't do with less advanced computers."
 
Computing offers students a chance to experiment.  It strengthens their understanding of the concepts by giving them a realm they can explore.  Says Stroyan, "Last year we had a student who complained that this course was harder than the one he had in high school.  But, he pointed out that this course is also the answer to the question, what good is it?"
 
Keith Stroyan, Ph.D. 
Professor 
Department of Mathematics 
University of Iowa
(319)335-0789
stroyan@math.uiowa.edu