This is all very detailed and complex. Most engineers I know have not used math beyond algebra or geometry in their day job careers. However, when faced with a problem, most engineers know where to look up info like the above. (The old cliche)
Modeling of physical systems was not taught in school. I claim it's an art. When I have performed this "art", only other engineers who were intelligent enough to have done it themselves have understood. Experiance? No. As a new grad years ago, I had to model a motor driver / antenna / radar system. I had no experiance but I pulled it off. It required understanding that a derivative is the change of parameter A w.r.t. parameter B. Hmm, I couldn't understand why that concept was so difficult to grasp by others. One of the closed-loop parameters was the angle of the target. This was in radians. Another parameter was the electrical phase lag angle of the motor current. This was in degrees. "You can't mix degrees with radians" some people shouted." I remember this vividy from decades ago. They were actually angry. "You certainly can", I replied. Luckily for this new grad, there were other engineers in the room who understood simple principles of math and the model was accepted.
I agree that the ability to physically model systems is a valuable skill. Having a good physical model can shed light on different areas of the design and accelerate system optimization and solution break throughs.
These skills are quite complicated to master and I think the main keys are gaining experience through practice and also having a good mentor.
The ability to produce an adequate model is very useful, but accuracy is omportant. One additional advantage of producing the model is that it serves as a "reality check" as it helps to avoid missing pieces and details.
BUT attaching real numbers to a model does get quite tedious, while some of them can be looked up, othhers must be calculated.THAT can be very tedious indeed, I have found in the past.
I agree. In many cases, the real numbers needed for these equations must be empirically determined through experimental measurement (and that can get quite tedious, time-consuming and expensive when a project is on a fast-track). Sometimes engineers want to take the time to run experiments to properly model the system, but management may not have the patience or commitment to allocate the needed resources and or allow the time to do it right.
Being able to procede without doing the modeling, or being able to do the modeling without doing all of the math, and getting it right, is the vaue of experienc, at least potentially the value. Knowing where you can't get away with assumptions is the biggest value of experience.
Interesting discussions. As a mechanical engineer who has made the transition into marketing and product development I can say that modeling (i.e. the mathmatical representation of the real world) is not confined to physical systems. Buying behavior, pricing scenarios, market response to financial pressures all lend themselves to modeling. Having the experience to look for these associations and the understanding to apply the correct modeling dynamics comes from my engineering background.
Scott, well said. Too many times, our engineering team delivered our product design on time, on cost and on spec. but the product didn't sell as well as anticipated. Why? Because the buying behaviors as you stated below were also not properly or accurately 'modeled'.
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