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1 Everything Is The Same

Welcome to my Coursera class Everything is the Same: Modeling Engineered Systems. I hope you

are looking forward to the class!1

One of the most fundamental goals of this class is to train you to synthesizedifferent aspects of

engineering skills. In particular, good engineers typically employ a combination ofAnalytical Rea-soning, Computational Skills, and Physical Knowledge to solve problems. The more critical the

engineering problem issuch as making sure that the power grid does not experience failuresthe

more important it becomes to combine these skills rather than just using one.

By Analytical Reasoning, I mean the ability to write down mathematical expressions that rep-

resent a physical system. By Computational Skills, Im referring to the ability to use a computer to

either evaluate or predict characteristics of a model that are too challenging to solve analytically.

And by Physical Knowledgepossibly the most important of the threeI mean thecrucialability

of an engineer to think critically about analysis and computations in the context of real, physical

knowledge about the world. This last piece can only come from experience, so in this class Im

going to rely on examples that you either already have experience with or examples that you can

easily reproduce on your own.

For those of you that saw the promotional video for this class, you saw the examples of the

power grid (a snapshot of which is in Fig.3) and the biomechanics of the hand.

Figure 3: A snapshot of the powergrid animation from the class promotional video.

Both of these examples are, of course, very complex to understand. Using physics-based mod-

eling, we can use analysis to come up with a model of the hand and we can use computations to

make predictions using that model, seen on the left in Fig. 4.

But what happens when we compute something that doesnt make sense, like on the right of

Fig. 4? When I look at this numerical simulation of the hand, I certainly dont think that I ever

wantmyhand to behave that way!

The reason we know that there is something wrong is because of our physical experience

we simply know that a real hand doesnt behave the way this movie suggests, despite the fact

that the analysis and computation was all done carefully. This physical knowledge tells us that

1If you are reading these notes after listening to the first lecture, you will notice that the class notes nearly perfectly

follow the online lecturesthis is intentional! However, these class notes will have many additional footnotes, like

this one, to explain and/or clarify concepts as we go.

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Figure 4: A simulation of the hand from the class promotional video. The simulation on the left

looks plausible, but the simulation on the right doe not!

there is something wrong with our analysis or our computations or possibly both, and synthesizing

physical knowledge into our engineering judgement is a critical aspect of engineering safe, reliable

systems.One of the challenging things about physical knowledge is that we all have different experi-

ences, so learning together is critical. Because of that, I really encourage you all to participate in

online discussions andif at all possibleI hope you will participate in in-person meetings with

other students taking the class. You can do this through organized meetups or other ways of ar-

ranging to meet with each other, and we will be hosting a meetup here at Northwestern University

every other week while the class runs.2 This social aspect of learning is, I think, critical to be-

coming fluent in modeling engineered systems and, simultaneously, thinking critically about that

modeling process.

In this class, you will learn different aspects of engineering modeling techniques. You will

learn Analytical Reasoning, including the importance of linear models, that differential equations

are nearly universal in engineering models, and that mathematical analysis of those models can

both help you understand systems better andmake your life quite a bit easier. To be prepared for

this analytical part of the class, you should have had some pre-calculus; in particular, you should

know that position and velocity are related by the time derivativethat the velocity v is the time

derivative of the position x.3 Aside from that, you really only need to be prepared to do some

algebra.

You will learn Computational Skills, including numerical integration methods that you will

implement in either MATLAB or Python and the use of vector representationsthese also make

your life quite a bit easier. You dont need any experience with programming for this part of

the class, but you will need to either purchase a MATLAB license or download Python, which is

free. We will provide short tutorials to help you get started and provide sample code to guide youthrough the class.

Lastly, you will learn Physical Knowledge, which will help you internalize when you can use

the mathematical modeling tools we are learning, when you cannot, and improve your engineering

judgment as a result. Whatever experience you already have will prepare you for this part of the

2The meetups will be organized through the Coursera website.3If you havent already, you should look at the calculus review we have posted to make sure you are familiar with

the ideas that are there.

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class.

Throughout the class, you will test the development of these skills by trying out the exercises

directly following the lectures and the homework. These will help you investigate the material in

more depth and solidify the material presented in the lectures.

Combining analytical reasoning, computational reasoning, and physical reasoning is an essen-

tial part of being an engineer, and I hope that as you take this class you learn how to synthesizethese skills for your future as engineers.

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