I’m convinced that in my job, I use 95% of the material covered in engineering school less than 5% of the time. Most of what I do boils down to on the job experience or falls in the category of project management. In many cases, not much would separate me from a talented hobbyist or tinkerer.
Of course, this makes me question the value of my education. Why did I spend all that time learning all that stuff? I’ve considered it for a while, and I like to tell myself that the 5% of the time I really use my degree is what makes me valuable as an employee.
In a tangential line of discussion, there’s also been a fair bit of talk in the news recently about the workforce, the number of engineers trained in the US, and why so many STEM students change majors. One line of reasoning suggests that it’s because classes are hard and students don’t understand why they spend so much time learning all that math.
That being said, I thought I could kill two birds with one stone and give examples of when I used my degree and all that calculus came in handy. So get ready, here are are some real life examples of an engineer actually using all that math.
Ok. This one was low hanging fruit. I use basic algebra and freshman physics all the time. That F=ma stuff? I’m a mechanical engineer. It’s my bread and butter.
I remember once I had to solve a center of gravity problem. Basically, I was asked to confirm that the center of gravity (CG) of the real mechanical part was in the same location that the computer model said it would be. This involved getting some scales, weighing the part, and doing some simple statics / force balance stuff to get the answer.
Now, when it gets more interesting is when you apply error bounds to the location measurement. There were three different scales at different locations and the CG was reported in a horizontal X-Y plane. You can’t just average the error bars of the scales, in units of lbs, and get an accuracy of location in inches.
The approach is to take into consideration the sensitivity of the final answer to each contributing scale’s error (and to be complete, the location measurement of the scales, but in this case that was well known).
In math terms, this means taking the function used to calculate the CG and taking the derivative with respect to each scale. Then the the sensitivity of the CG measurement to each scale becomes apparent, and the errors can be RSS’d together.
These things actually are useful. So we were studying Taylor series expansions freshman year and going through expansions of trigonometric functions and the teacher explained that if you didn’t have a calculator and you wanted to solve for sin(x) in the neighborhood of 0, you could plug it in to:
sin(x) ~= x – x^3/3! + x^5 / 5! – x^7/7! ….
with terms extending just so, until you had an answer of sufficient accuracy.
Now, that’s an eye roll worthy explanation if you ask me, because frankly, in this modern world, when will I be solving problems without a calculator nearby? What I wish he had said, was that it turns out that Taylor series are particularly useful for making non-linear things, like trig functions, linear.
For example, if you’re developing a control system using state space techniques, you end up using a lot of matrix math and linear algebra. (There’s that math again!) Linear algebra, being linear, has trouble with non-linear things, and so there you go. Linearize with a Taylor series.
This one was a bit of a stretch, because I haven’t had to solve Diff Eq’s outright, but it has been important that I understand them.
One of the bugaboos about Finite Element Analysis of mechanical parts is the need to verify computer models. One rather useful non-destructive method relies on vibration analysis. The physical part can be tapped with a (small, calibrated) hammer and it’s resonances measured. These resonances can be compared to the resonances of the computer model.
After a hammer test, it is typical to use physical measurements of the model to correct difficult to predict properties, such as damping. I was working through one one of these test / model correlation exercises, when some frequency dependant damping was making it hard to get the amplitudes of various resonances to line up.
An understanding of the differential equation that governed the vibration response and how the finite element analysis software was solving it was essential to doing my job.
I suppose I’ll finish by saying that although math classes can be hard, it certainly is useful. In many ways, I wish I could go back and teach things differently. Calculus was first developed, for example, to help predicate the motion of the planets and stars, which lead to important navigation and map making techniques. That in turn, made it possible to send a ship from one side of the world to the other while reducing the chance of getting lost or sinking. Which of course meant making boatloads (ha!) of money. Calculus was not simply some mathematical exercise, but a technology of immense economic value. And that’s pretty cool. But it was never taught to me that way.
How do readers relate? What has been your experience with math in the workplace or in grad school? Do you use your degree 5% of the time, or more?
Thanks to macattck for the protractor picture.