# Coursera EITS

## Everything Is The Same: Modeling Engineered Systems

I taught the Coursera class *Everything Is The Same: Modeling Engineered Systems (EITS)*—an online engineering class based on a first-year course in the McCormick School of Engineering at Northwestern. The class opened 9/23/13 and closed 11/27/13 and and then ran again in early 2014. Why did I create an online class? First and foremost, I was interested in how much background students really need to be able to learn systems theory (by which I mean the modeling of systems using linear ordinary and partial differential equations as well as the solving of those equation using either numerical or analytical solutions). We tend to treat systems modeling as advanced material, often not seen until the senior year, but the content in a systems modeling course really only requires minimal exposure to calculus. So, as the debate about Massive Open Online Courses (MOOC) emerged, I became interested in running a Coursera class. My other motivations included the opportunity to train students earlier in their academic careers, recruit students we have historically not been able to recruit, and assess students in new and potentially more meaningful ways as part of our admissions process.

*EITS* covers basic modeling of mechanical, electrical, and chemical systems. It starts with the definition of the derivative and through 24 lectures averaging 6.5 minutes each ends with the time-varying wave equation $\frac{\partial^2 C}{\partial t^2}=k\frac{\partial^2 C}{\partial x^2}$ (a linear partial differential equation found throughout engineering analysis). Along the way we see Newton’s laws $\sum F=ma$, superposition, Kirchhoff’s laws $\sum V=0$ (and $\sum i_{in}=\sum i_{out}$), convolution, and the time-varying heat equation $\frac{\partial C}{\partial t}=D\frac{\partial^2 C}{\partial x^2}$ (another linear partial differential equation found throughout engineering applications). Importantly, the class only assumes students have minimal exposure to derivatives; no linear algebra or advanced calculus is assumed. As a result the course is challenging, but prepares students for the rigorous classes they will see later in an undergraduate experience. The class started with almost 18,000 enrolled, ranging from high school to postgraduate students. So far during the eight week run of the course the online students seem pleased with the content as we have received almost exclusively positive feedback. The course content consists of a combination of 1) lecture videos of me talking and writing, 2) typeset course notes, 3) my graduate students discussing how the course content relates to their research, and 4) experiments we hope online students will do at home. I am also using the online content in the corresponding Northwestern course I teach as part of a “blended” learning strategy.

#### Why do students take MOOCs?

For postgraduate learners and industry professionals online classes may help deepen pre-existing understanding, spark interest in new fields, or synthesize their knowledge. For the high school students taking this class, technical content may help them see the real-world utility of calculus, programming, and physics. But the range of reasons for taking this MOOCs is far beyond what I expected. In preparation for a talk I gave (October 2013) at the National Academy of Engineering on MOOCs in engineering education, I asked my online students why they are taking the class. Some of the reasons included:

- preparation for job interviews
- preparation to continued formal schooling
- investigating whether going back to school is worth the time/expense/effort
- supplementing higher education that has been halted due to government challenges
- engaging in technical collaboration
- engaging in social/international collaboration

The key point is that people took the class for all sorts of reasons, many of which were great, and most of which I had not anticipated.

#### Physical Experiments in Online Classes

The course also included demonstrations—experiments that students could do at home. The total cost for the materials was roughly \$25; though the experiments assumed access to a computer and a mobile phone (or something else capable of taking digital pictures). These included system identification for simple elastic bodies, chemical diffusion, and electrical diffusion in RC circuitry (the latter two are pictured below). These demonstrations were then replicated at home and generalized by online students who wanted to pass the class *with distinction.*

* *

(chemical diffusion in the form of dye diffusing in water) | (electrical diffusion in the form of charge diffusing through 8 resistor-capacitor pairs) |

The online students did terrific generalizations with relatively little physical infrastructure; example projects from online students included eddy current damping, heat diffusion on a stove, and molecular mechanics using data found online.

#### Flipping the Classroom

Unlike the online students, who are taking the class for many different reasons, my students at Northwestern are taking the MOOC as part of their credit for my on-campus course. It is obvious that they are getting tremendous benefit from the at-home use of the online content. Evidence includes that the students at Northwestern are asking much deeper questions than in previous years. What does it mean, physically, for a system to be linear? How do we know that exponential solutions are the only solutions to linear ordinary differential equations? What does it mean for a linear affine system to be linear? Why is the heat equation a linear equation? These questions prepare students for what they will see in their later, more advanced, coursework.

*EITS* will likely run again in 2014. When I run it again, I hope to more aggressively recruit high school students into the class. Moreover, a key challenge is getting more students to "opt in" to doing the at-home experiments. But for now the conclusions are reasonably clear; systems theory can be effectively introduced much earlier in on-campus curricula as well as online settings. Doing so will prepare students for both modeling, signal processing, and control they might see later in their academic careers.

My blog prior to my talk at the National Academy of Engineering Frontiers of Engineering Education Symposium can be found at NAE-FOEE site. An op-ed I wrote for the Pacific Standard Magazine can be found here.