Do engineers really need to understand calculus?

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In summary, the class discussion revolved around whether or not engineers use calculus in their everyday work. Some argued that since most real-world problems can be solved using numerical methods, calculus is not heavily relied upon. However, others pointed out that understanding calculus is important for setting up differential equations, which are frequently used in engineering analysis. Additionally, calculus allows engineers to have a deeper understanding of physical concepts and can help distinguish a good engineer from a bad one. Ultimately, the use of calculus depends on the type of engineering work being done, with those developing new systems likely needing it more than those utilizing existing devices.
  • #1
Farina
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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?
 
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  • #2
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 won't use too much.

If you're developing new systems, then you will probably need it a great deal.
 
  • #3
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.
 
  • #4
Farina said:
that the vast majority of real-world situations
are analyzed using numerical methods.

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?
 
  • #5
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.
 
  • #6
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.
 
  • #7
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.
 
  • #8
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.
 
  • #9
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.
 
  • #10
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,
Once you learn calculus, the relationship between velocity and acceleration, for example, takes on a whole new meaning.

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.
 
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  • #11
enigma said:
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 won't use too much.

If you're developing new systems, then you will probably need it a great deal.

-----------------
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.
 
  • #12
this seems to be what I'm hearing most...

Integral said:
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.
 
  • #13
very well said... I'll bring this to class on Friday (and will
certainly reference the source -- thank you).

Q_Goest said:
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.
 
  • #14
well the integral is used when you dip into differential equations

most engineers won't 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
 
  • #15
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.


Tom Mattson said:
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?
 
  • #16
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.

Farina said:
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?
computational
 
  • #17
Farina said:
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.

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.
 
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  • #18
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.
 
  • #19


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.
 
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  • #20


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 loge, 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 loge have this effect?
 
  • #21


Necropost alert! (look at the date on post #18)
 
  • #22


I left engineering to do math, myself. It could be that engineers don't explicitly use calculus all that much. However, as a former EE student, I can say that you definitely can't UNDERSTAND EE without calculus. Electromagnetism has tons of calculus. So, you can't understand the laws that you are working with without it. Also, circuit analysis is basically differential equations and calculus, but it's kind of swept under the rug because Laplace transforms and phasors can convert it into algebra. But, if you don't want to take it as a big black box, you are going to need calculus to understand it, and indirectly you are using it anyway because no one would have come up with it in the first place without calculus. Signal processing. Again, calculus is a big part of the theory.

Computer engineering, maybe not so much.

Maybe engineers tend to be people who are okay with just using blackboxes, and that's why I left EE, but if you're not one of those engineers, calculus is pretty good to know. Personally, if I ever went back to engineering, I couldn't stand to use black boxes. I have to know why everything works. And some engineers are actually like that, I think. Rare, but they do exist. Most of them probably go to grad school where there's a lot of theory.

Of course, a lot depends on what you are doing.

I know sometimes a theoretical approach is counter-productive in engineering. But, at the same time, I question whether not understanding calculus would be make for a good engineer, since that would limit their understanding considerably. The question of whether they should use calculus is slightly different from the question of whether they do use it. I would say, at the very least, they really do at least need to take a couple classes on it and maybe one on diff eq, just so they are aware of it, which is the current system, and I hope it doesn't change, at least as far as that is concerned.

I never worked as an engineer, but I know, as a former EE student, calculus is all over the place in EE, at least in the backdrop. I mean, I can open up my computer and see capacitors. The generator at the power station is cranking away based on Faraday's law, which is a differential equation. So, in just about any electrical device you see, there's calculus lurking there on some level.

As far as numerical methods, what's the most commonly used numerical method? Newton's method. Guess what it's based on? Calculus. So, the relevance might not be that you actually have to take a lot of derivatives and integrals. It's in the concepts.
 

What is calculus?

Calculus is a branch of mathematics that deals with the study of change and motion. It is divided into two main branches: differential calculus and integral calculus. Differential calculus deals with the rate of change of a function, while integral calculus deals with the accumulation of quantities.

Why do engineers need to use calculus?

Engineers use calculus to solve real-world problems involving rates of change and optimization. It allows them to analyze and design systems that involve motion, such as bridges, cars, and airplanes. Calculus is also essential in understanding and developing theories in physics and other engineering disciplines.

Do all engineers need to use calculus?

While not all engineers may use calculus on a daily basis, a strong foundation in calculus is necessary for all engineering disciplines. It provides a fundamental understanding of mathematical concepts and problem-solving skills that are applicable in various fields of engineering.

What are some specific applications of calculus in engineering?

Some examples of applications of calculus in engineering include determining the stresses and strains on a bridge, analyzing the trajectory of a rocket, and designing electrical circuits. Calculus is also used in the development of computer algorithms and software for engineering simulations and models.

Is calculus the only math that engineers use?

No, engineers use a variety of mathematical concepts and techniques in their work, including algebra, geometry, trigonometry, and statistics. However, calculus is considered a fundamental tool in the field of engineering and is used extensively in many applications and disciplines.

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