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.

## Algebra

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.

## Derivatives

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.

Boom. Engineered.

## Taylor Series

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.

## Diff Eq’s

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.

## Summary

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.*

Aside from math..yes I would have to agree that hands on is what any job is about. School is there to teach you to think but it will never be better then hands experiance

Nice article, I find myself agreeing with you on the point that the few times you need to use your degree makes you worth it to your employer. For me personally (BS/MS EE degree), I find myself using the math heavy side of my degree maybe 10% of the time though it varies from week to week.

Algebra – definitely used every day too

Derivatives – couple times a week as required while I study capacitor/inductor waveforms and also as a personal sanity check.

Integrals – a few times a week too at least now while I’m temporarily helping on a project. Finding the reverse recovery charge on a diode requires some integration though nothing too challenging.

Diff Eqs – not so far though I’m still only 6 months in.

Fourier Analysis & Bode Plots – When I’ve needed them so far it’s everyday for a week or so then not again for a while.

As I begin designing new regulator modulator architectures and chip features along with SPICE modeling I’m pretty confident I’ll have to rely on more and more of my degree to get by.

Math does indeed come in very handy from time to time :-). A lot of what I learned was taught without context; it was math for math’s sake. I wish I had a better understanding of why I was learning what I did.

Sometimes I think it’s because I had math teachers teaching math class and not engineering professors.

One thing I did not mention in the article is that undergrad math is absolutely essential for grad school.

Yeah all my intro math and physics classes were almost entirely taught without application. It was extremely frustrating when we happened to be covering a topic like basic circuit analysis and I was screaming in my head “No one does it this way!”

That being said I also think having a strong background in math is essential. It’s relatively easy to see the applications if you know where to look and have a genuine interest in what you’re learning.

As an engineering professor, I guess I should argue that I use the stuff every time I teach class. In the real world though, at companies and in the research lab, I use the knowledge from general chemistry and analytical chemistry classes all the time as well as transport phenomena. Occassionally I use reaction kinetics. Most of the other stuff ,not so much. I agree with Setty Associates, the hands on stuff is critical, especially in chemical engineering where it’s not as easy to tinker around the house. This is where it drives me crazy to see chemical engineering students not having/taking chemistry labs.

I want to put forth a stronger argument though for why the $100k, these days $200k is worth it. The thing is, you don’t know ahead of time what your job will be or if you will ever change fields during you career, so you don’t know which 5% you will be using. Even though I never touch it, lots of my former classmates are doing thermodynamic calculations regularly, at least they did when they started. By now most of them are managers. And if you take all the courses, then the cost adds up. I’m constantly getting solicitations from professional societies to take 1-2 day courses on a specific topic where they charge over $1000. If you don’t think that price is outrageous, then the $200k shouldn’t seem so outrageous either. The problem is that the tuition is going up much faster than inflation and salaries, but that isn’t an argument against getting the degree.

I think I could debate this point for a while. Particularly over a beer. In a bar.

“Perhaps more than English or history, STEM subjects require an enormous amount of foundational learning before students can become competent. ”

-Washington Post,”Want Your Kid to be a Scientist”, 19 Jan 2012

While it certainly is true that you don’t know which part of your degree you will use, and there is clearly A LOT to learn, it’s worrisome to me that the great bulk of my time on the job is spent NOT using my degree. I want classroom education to better reflect what I do at work.

I have a vague notion that the solution is to have something like an apprenticeship, which I imagine to be like an internship or a co-op, but with more structure, or that runs in parallel with your coursework.

Not to invite myself but count me in if this bar conversation comes to fruition lol. I’d love to weigh in with my two cents on making coursework more inline with day to day work life.

>Sometimes I think it’s because I had math teachers teaching math class and not engineering professors.

– Valid point.

A good friend of mine is doing his Master’s in Mechanical. The next stop is a Ph.D because he’s got his eye on teaching. Will pass this article along to him.

Kate

Some would argue that the value in an engineering education is not in the particular classes you’ve taken, of which you may actually only use a small fraction on the job. Rather, the value is that it trains you to think like an engineer – to have a certain thought process that is brought to understanding, analyzing, and solving problems.

Personally I think this view is partly true, but this disciplined thought process one starts to learn through an engineering degree program usually requires further maturing in the work environment.

Regarding not using all or even much of one’s degree on the job: the fundamental problem as I see it is that degrees are general (even at the level of electrical engineering versus mechanical engineering versus etc.), whereas jobs are specific (propulsion thermal control engineer, electronics radio frequency interference engineer, etc.). It would take a huge specialization of degrees to make it where the bulk of your education directly applies to your job. And then that’s the only job you’d be qualified for.

Exactly.

I started out as a electrical / computer engineer working with embedded systems. After a few years I realized that I needed to change to something else before I went crazy. I managed to turn myself into a rough version of an EE specializing in RF systems, and even that required taking more classwork that I didn’t have the first time around. There is no way I could have made a shift like that if all the classes I had taken for my undergrad had focused strictly on software and computer architecture.

An Engineering Education is only a small percentage of what you need to do your job. Much of what you need day to day will be learned as you are doing the work. Hopefully, your company will not have traded off mentoring for productivity.

The amount of coursework that could be taught in an engineering program is huge. The engineering department has a very hard time deciding which course materials to cover and which to exclude. Even with limiting the amont of material that is taught, an engineering program is like drinking from a fire hose. Once you have learned something, even though you have forgotten it, you will learn it much more quickly the next time.

Technology is changing so rapidly that it is difficult for universities to keep their courses up-to-date. And the half-life of an engineering education surely has become less than 5 years by now.

Don’t remember where I read it, but someone made the comment to the effect that a working engineer was continuously learning the equivalent of getting a masters degree every two years.

So there is a good reason that an engineer only feels like they are only using a small percentage of what they were taught.

I was one hundred percent against you until you said calculus. Then, I was on your team.

I believe I was extremely lucky in my career. As a design engineer, I believe I used more of my education than any of my fellow students who worked in operations or sales or other areas.

The ultimate example occurred about a dozen years into my career. I had to determine the problem with a five stage, multiple effect evaporative crystallizer. I consulted the company’s expert in fluid flow/mathematical analysis and he said he was able to model a single crystallizer using differential equations and get an answer in four hours. Using a computer.

Ah ha. says I. Computer don’t do differential equations. They do incremental analysis. I immediately (it took an hour or less) developed a Basic Language program on the computer which did a material balance of each one minute increment, (Excel could also be used.) went to the next increment and so on. In less than four hours I had the answer. The system took four hundred hours to come to equilibrium. Who would have guessed?

One of the posters had the answer. Engineers need to know the concepts of calculus, but not the details.

Shortly after my graduation, I heard industry people saying academics were out of touch. They still are.

I’m a electrial engineer having 28 years of design experience, 22 of those working as an independent. Every single thing I do every day, from circuit design to PCB layout to embedded C programming, to PLC system integration, to CAD design, FPGA design, to CAM machining, to running a business, to proramming in many languages as needed, all of this I learned entirely on my own, (no colleagues, no seminars, no courses necessary) after I graduated. That is the value of the engineering degree. I was not intimated by anything. My only regret, and what I would in retrospect advise new engineers is to suck it up and do it the easy way … work for a big company, or the government (the same thing.), relax, and be a well paid cog.

🙂

Frank