# How much Calculus?

How much to engineers actually use calculus? What is the proportion of Non-Calc vs. Calc computations?

Depends what you’re working on.

If you’re dealing with motion, you’ll be using it quite a bit (position-velocity-acceleration). MEs deal with motion a lot…

Controls and circuits use Differential Equations quite a bit; that’s only learned after Calculus 2.

Statics and solid mechanics tend to use integrals and the like sparingly.

As far as proportion, it depends on what you’re dealing with. You could probably get through 2 years in college without much calculus, but beyond that, expect about 25-30% of the work to involve calculus in some way, shape, or form; you might even be turning differential equations into algebraic equations.

Results may vary.

At my school, they start you with calculus your very first semester and start applications of it the second semester. I suppose those are all just “math” or “physics” courses rather then actual “engineering” courses but they are required to be taken first at my college. To the best of my knowledge, there are two general approaches to the engineering degree. Some like to throw a bunch of theoretical math at you so that your engineering courses can go into more depth. Others like to save alot of the theoretical math until half way through so you already have real world examples they can use within the math course themselves.

Same with mine. Like I said, for about the first two years (while you’re still in Calc 1, 2, and 3 and Diff. Eq.), you can probably get by with very limited calculus (physics, some other stuff). Looking at the ME departmental prerequisites, though, if you don’t have Calc 1 and Calc 2, there are three courses that you won’t be allowed to take in sophomore year: Sophomore Design, Dynamics, and Thermodynamics 1. Most of the math that those courses use is algebra or trig or something like that, so you might be able to get by for a while. Once you get up into junior-level courses, though, you need to be able to do calculus or differential equations at any time.

If you’re an engineer[ring student], you’ll use calculus frequently enough that you should know it or be able to pick it back up with a little review. I can’t think of an engineering discipline that doesn’t use it in a lot of what they do.

Don’t be intimidated by calculus.

Check out the first 47 seconds of this video,

and the first 70 seconds of this video,

for one reason why calculus has gotten a bad rap.

Calculus is not difficult to learn and use, especially if you care more about the application (engineering emphasis) than the theory (math major). With all the CAS tools available today (like maxima), all the grunt work (like finding integrals) is gone and it’s actually fun.

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I teach math and Physics as my day job and moonlight as a robotics coach. I can safely say that “hard” subjects like Calculus and AP Physics B/C become a heck of a lot easier when you have mastered the algebra skills required to get to the applications that are the focus of the respective classes. Don’t worry too much about how much calculus is needed. Math is just one tool. Real life problem solving skills are much harder to learn.

I’m an Environmental Project Engineer and I’d say that my calculations are 99% non-calculus. But that’s more because I’m implementing systems rather than designing them. But I loved those days of using calculus to determine the design needs for fluid flow and air transport! Math is FUN!

[3rd Aeronautical Engineering Student Perspective]

I haven’t walked into a class this semester that didn’t use calculus.

That said, you find in engineering that most integrals are too gross (or time consuming) to do by hand. As Ether said, you’ll have Mathematica, MATLAB, a calculator, or Maple to actually do the integration. In my experience, you will be expected to know what an integral means, what a derivative is and be able to integrate polynomials and sine/cosine, but that is about it. There will not be a surprise test question asking you to find the volume of some complicated curve rotated about the x-axis.

Engineering is all about assumptions, and you’ll find that lots of these assumptions turn integrals into algebra. Probably 80% of my Aerodynamics notes are integrals, but only 30% of the homework is.

My two cents: I use calculus occasionally, but the most important thing I learned was how calculus works, fundamentally, as I use numerical integration most commonly. I’m a mechanical engineer, FWIW.

With this being the digital age, some study of the matrix math can be very important. Matrix algebra at a minimum and Matrix calculus for those who want a little more pain and suffering. If one develops the ability to deal with N dimensional matrices, solution to complex problems can be easier. Most people are stuck on either a vector or a table. Some can deal with a 3d matrix. Most give up on N dimensional.

I’ve been a practicing mechanical engineer for almost 9 years. I have never directly used calculus or differential equations in real work. I tend to use Linear Algebra quite a bit however.

I’m still glad I learned the math to understand where many of the formulas that I regularly apply come from but in reality I don’t use the math directly in my work because I’m not on the heavy analysis side of the work.

I’m a Mechanical Engineer I use Calculus regularly in my work. Frequently I have to derive my own beam equations for unique situations that aren’t available in Roark and that requires differential and integral Calculus. Also impact loads require performing an energy balance which is generally done with Calculus. If I want the moments of inertia of a section I usually just pull it out the CAD model, but if I want it parametric then I need to derive it with Calculus. Sometimes there are easier ways to get the answer but if you want to understand the sensitivity of the answer to variable parameters you really need to derive the equations yourself.

Been in process design engineering for refineries for over 2 years now. I don’t use calculus myself. However, the computer I work with uses it (and linear algebra) a good amount.
I have friends that are in research that use calc themselves quite frequently. So, it depends on what you are wanting to use the engineering for.

After almost 30 years since my EE degree, I can’t say I use Calculus much. But then again I was never a design engineer, I have always had positions where I supported existing product. These days I write training for a living.

But having said that, and noting that although I see the beauty in math and how it describes the physical world, knowing and understanding calculus was absolutely essential to my career. You see, in order to support a product (or write training about it) you must understand the design. And for that, you need to know calculus, otherwise you get lost pretty quick.

Some advice I wish I had as a college freshman: If you don’t understand it, or are struggling to keep up, ask for help. Sometimes you need to look beyond your professor (there may be a personality difference), but once you find someone who can explain it in a way YOU understand, it gets a LOT easier.

And don’t limit yourself to instructors… purposely seek out and develop friendships with other students in each class who are serious about doing well. Make learning the subject material part of your common interest.

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With middle school roboteers no Calc, lots of geometry. We engineers have decided that PI=3 for all calculations. In a 12’ space the .14159 part isn’t making any noticeable difference.

In my job, lots of basic math and a ton of stats (project manager). Most along the lines of “probability of meeting the deadline on Tuesday is none.” After slogging though calc classes, I’d rather have the stat classes.

Gary mentioned matrix math, I did a ton of that when hand crafting graphics routines in hand crafted Fortran and assembler. Cycle times were slow and you had to wring everything out of each instruction. The Winter Session Matrix Math class saved me in some tough situations.

It depends on why you are asking. If you are attempting to justify skipping out on one moment of calculus, you will just be shooting yourself in the foot. The more math you have available to you, the more interesting things you will be able to do in your career. If you are asking whether you should take additional e.g. statistics instead of additional calculus, let us know what you are interested in.

Gary said it better than I could:

In my (brief) career, I’ve used a lot of calculus, algebra, and linear algebra, but the math that has proved most useful to me has been optimization theory and numerical methods.

My favorite thing to do as an engineer is to describe my system as a series of equations (see Gary’s post), massage those equations to describe what I want my system to do, and then translate it back. Or, even better, having a machine crunch over those equations and optimize them for me. Any weekend adventure you take is made better by the knowledge that something is doing your work for you while you relax.

Here in Indiana, we made a law stating this a while back. Needless to say, it didn’t go over too well for alot of things. I find the pi button works just as well as the 3 button on my calculator and have yet to find a need to round until the end. I’m not saying rounding won’t work for some things, but to all students reading this beware. Teachers do count off.

Jason

Upper classmen can be a great resource. I was struggling for a whole quarter with some math for Physics. A guy a year ahead of me saw what I was struggling with and gave a very simple explanation of what was going on. It took about 15 minutes to go from failing to a C. I still wish I had talked to him before Finals week.