Do Engineers Use Calculus?? A heated debate broke out in class today. The topic was whether or not engineers use a lot of calculus on the job. We are talking about practicing, professional engineers, not engineering students. I'm on the side that says NO -- the class of real-world problems that are addressable using calculus is very small; that the vast majority of real-world situations are analyzed using numerical methods. The other side disagreed and suggested, for example, that electrical engineers use a good deal of calculus since in many cases the theoretical situation they are looking at matches the real, physical situation. What do you think?
Depends on the work you do. If you're an engineer which takes existing devices and utilized them (sort of like building systems engineers), then odds are you wont use too much. If you're developing new systems, then you will probably need it a great deal.
Many Mechanical engineers do little mathematical analysis, they simply over design so that they are not near any questionable boundaries. When they do apply math they have a book full of canned formulas to draw on. When analysis is done it takes the form of a differential equation, rarely in the real world will a differential equation have a good simple closed form solution, therefore numerical analysis. BUT... setting up the differential equation requires knowledge and understanding of calculus. Even if you do not ever solve another integral in your life after completing college the understanding of nature that you gain in calculus can be and will be applied frequently if you go into a career in engineering.
Yes, but how are you going to program a computer to do calculus, if you can't do calculus yourself? And are you willing to trust your (expensive) real world system to black box that does numerical analysis without checking that black box against some known cases by hand?
You need Calculus and Differential Equations at least to get through the classes. Any Engineer in or outside of school is expected to know these well. Work lots of problems to get good at it.
I might add one thing: The job market is bad right now. Not all engineering graduates hold engineering jobs (this one included). I teach math at a community college, and several of my colleagues here are engineering grads. If they did not remember their calculus, they'd be collecting unemployment checks. Math is simply part of the engineer's toolbox, and it should be that way.
A great many physical concepts are defined in terms that are only precise if you use calculus. Thus, rather than always actually calculating with calculus one is often dealing with concepts like magnetic flux, which are ill defined without it, even if you don't solve an integral.
I can only think of three modules out of 25 I've done in my engineering degree which have not used calculus to some extent. Couldn't agree more with Tom about maths just being a tool. It's like having a massive hammer, it's no good unless you know how and when to use it.
I agree with pretty much everything said and would also like to add that Calculus also falls under the category of general science/engineering knowledge. Once you learn calculus, the relationship between velocity and acceleration, for example, takes on a whole new meaning. Tools like calculus are what cause scientists and engineers to look at the world around them in a different way than everyone else. And if you simply memorize the formulas, you won't get that understanding - and having that mindset is one of the big things that separates a good engineer from a bad one. I call it "voodoo engineering" - its how you can give two engineers a piece of information, one of them looks for a formula in a book to figure out what to do with it, the other just instinctively knows what it means.
Farina, I'd have to agree with you. I consider myself a highly analytical type with over 15 years of engineering experience (BSME). I design pumps, compressors, cryogenic equipment and a vast variety of things at work. Each part of a machine gets a stress analysis, fatigue analysis, much of it gets a dynamics analysis, heat transfer analysis, thermodynamic analysis, fluid flow and pressure drop are things I've written papers on. The bible for stress analysis, Roarke's, and the bible for fluid flow, Crane paper #410, have virtually nothing in them which requires calculus. I've had to actually solve an integral maybe once every few years. It's so rare, that if I didn't know it, I'd not be missing much. But that's not really fair either, because as Russ points out, You can use the basic concepts of summing parts as is done in calculus using numerical methods, so the concept is what's important. Without that concept, you really can't function. Knowing how and why you need to analyze something numerically is exceedingly important if you're into the analytical side. Calculus doesn't necessitate the use of integration, solving differential equations, etc. I know of maybe 1 engineer out of the hundreds I've met that truly is comfortable with writing those types of equations, and he's retired now. Smart guy, but that's the exception IMO, not the rule. On the other hand, if you're a project engineer, engineering manager, etc... calculus is a long forgotten word.
----------------- Such as... ?? What kind of examples of real-world products can you think of that were developed with the aid of a great deal of calculus?? ----------------- I'm at a loss to think of too many real-life examples of practicing engineers using calculus extensively as part of their job function. I sent this question to the director of Fuel Cell Research for Visteon (Ford Motor Company's spun-off supplier -- a $27 billion company). He himself is a EE. He was emphatic that a background in calculus was very important for providing an important theoretical background, but stressed what I hear all the time from physicists: virtually no interesting real-world physical phenomena are solve-able analytically. They are, rather, solve-able using numerical methods. Makes me wonder why numerical methods aren't stressed a lot more in ugrad and grad engineering courses.
very well said... I'll bring this to class on Friday (and will certainly reference the source -- thank you).
well the integral is used when you dip into differential equations most engineers wont admit this but there are shortcuts they could use to cut the calculations in half if they used more advanced math, but if a simpler math works well they'll stick with it. most statics is geometry and basic physics. although you could use calculus on it and get more advanced models
Your typical ME, CE, EE, etc. won't be spending time programming a computer. Your second point, however, is one I agree with: knowledge of calculus provides valuable insight to the basis of many numerical approaches, as well as the workings of nature.
We had a similar conversation in a physics forum. I think that engineering students should be made aware that once they begin their professional engineering careers they will be relying much more on computational than on analytical methods. This insight would better them and increase their chances of on the job success. computational
Numerical models and numerical methods begin with calculus. Most engineers may use tools, i.e. numerical methods, which have already been developed. My organization develops new models and applications, therefore we 'get back to the basics'. Engineers involved in fundamental R&D of technology probably use calculus more often than those involved in direct applications of technology.
Even if you don't use it, you must know it. A doctor may never treat a heart attack, but he must know how if one comes up, or he's not a Doctor.
Re: Do Engineers Use Calculus?? I am an electrical engineer and I have been working in the utility industry for 3 years. I can say honestly say that neither me nor my co-workers ever use Calculus on the job. As a matter of fact engineering education only gives you the tools to learn. The thing that you need the most from school are the concepts from some of your engineering courses. The unfortunate thing is that many important concepts that are needed get buried beneath math. This is because most engineering professors have never work in the field as an engineer. There is a tremendous difference between a professional engineer and an engineering professor. Professors spend much of their time doing research on many things that have not been fully tested or proven. A professional engineer have actually witnessed their projects go into service and work. My advice to engineering students is to try to enjoy your courses and do not get lost in math details and calculations, the concepts are the most important. Also keep in mind that in the field engineers are more interested in understanding how systems or devices work. You will not be sitting in a cubical doing calculations or solving some mathematically based problems. The problem solving will be applied to getting things to work or producing a final reliable product, not trying to get some correct numerical value. Also remember math is a tool and means to an end.
Re: Do Engineers Use Calculus?? Let me begin by admitting that I have no engineering degree, nor have I ever worked as a professional engineer. However, I have analyzed rockets, and I've always used equations employing log_{e}, to solve such calculus-based relations as: the effect of constant acceleration in producing constantly increasing velocity; the effect upon the above of the constantly decreasing mass of the vehicle due to fuel consumption; the effect of aerodynamic pressure applying drag against the vehicle, first increasing as the vehicle gains velocity through thick air, and then decreasing as the air gets too thin to resist increasing velocity applied to decreasing mass; the effect of decreasing gravitational attraction upon the vehicle by the Earth as the vehicle moves further from Earth's center of gravity. *** What I'm curious about is why does log_{e} have this effect?