Engineers: ever actually do calculus by hand on the job?

Dear Jeff Quinn:
I have done so on about four occasions, in 15 years. Just before I found out the results were available in a table somewhere.
E.E. "Doc" Smith (no relation) did integration in his head...
David A. Smith

It does seem tedious. Enjoy the partial differential equations.
Engineering jobs tend to be quite repetitive in what's required to get the job done. But Engineers move from job to job and sometimes get propmoted before they move elsewhere. So there is some change.
Academia is not a true reflection of the real world. Academics can easily test your knowledge; but have much more difficulty in testing your _understanding_ in an exam.
Engineering is essentially not about what you actually know; you observed already that facts are easily looked up; Engineering is about understanding and getting to understand how things work, and making that fit the required solution.
Do you? Good. I spent 3 weeks doing novel structural designs that required the application of calculus. An actual solution was only possible using numerical methods to solve the second-order partial differential equation for particular values of variables.
A pure numerical solution wasn't possible because I had to find an expression for maxima, based on a number of variables. The necessary combination of fundamental theory and the resulting dozen of applicable formulae in combination provided an expression of how the variables interacted as a partial differential equation. In doing so, it provided a quantified insight into the behaviour of the system.
Mathematics in all its forms is just another of the tools which Engineers can use to do their job. The greater the variety of tools you understand how to use, the more likely your chance of arriving at a good, competitive solution.
You don't atually have to be an expert mathematician; just appreciate what there is to use to be able to choose the best tool for the job.

From: snipped-for-privacy@onid.orst.edu (Jeff Quinn)
Sounds pretty standard and reasonable to me. Calculators and notecards have nothing to do with Calculus.
The idea is for YOU to learn Calculus and what you can do with it.
You'll find that different professors have different rules for the test they administer. Some allow notes, etc. Some don't. For many... it depends on the particular class they are teaching and sometimes even on the mood they are in.
I've used Calculus plenty ( integrals and all ). There are LOTS of uses for it on the job. No.. I don't think you know the answer to this one at all.
Dan :-)

I seldom have occasion to do tricky integral calculus like integration by parts etc. But I frequently find that describing a problem in the form of an integral or differential equation is helpful to see how the problem actually works mathematically (what terms dominate the behaviour of a system etc). In order to do that, it is necessary to understand (sometimes with a little review first) how the underlying calculus works. There are many times when there is no closed for solution to a problem and even if you posed a problem in the form of a calculus expression and relied on the calculator to solve for a particular case you might miss the point. Only working through the problem in a more symbolic form really illustrates how the physical system works. Once that is understood, letting the calculator crunch out a particular solution is probably OK. Without the hard part, the main point can be lost.
All this having been said, this is hardly a daily affair.
As a fellow OSU alumni I say suck it up and do the math. ;)
Unless the ME program at OSU has changed drastically since I was there, you have 2 more years that will include physical systems described in terms of calculus on an almost daily basis in materials, dynamics, heat transfer, etc etc. Don't get too attached to that calculator.
Jon Juhlin.

You are learning more than just how to use tools. The ability to memorize facts and procedures and the ability to use this knowledge to solve problems is just as important as the specific tool (calculus).
Solving those integrals takes some ingenuity sometimes.

Ok guys, thanks for the replies, I think I see where you are coming from.

Yeah, remembering the equations isn't as important as the theory and application. The field of Mechanical Engineering you want to go into might not require a lot of calculus, but other fields do.
The biggest advantage of calc is that you understand more of the "why" behind things, instead of just memorizing the end result like a parrot.
Structural analysis, for instance, uses a lot of calculus if you do it by hand. The bending moment in a beam is a double integral. Sure, you can look it up in a book, or you could also run an FEA... but if you don't understand the theory, then what makes you different than a high school grad looking it up?
Dave

Oh yeah, one more thing... in vibration analysis we use it A LOT. The reading off an accelerometer is just acceleration. Using something like a Newton's method, you can calculate the velocity and displacement.
Also in heat transfer, if you want to know the transient temperature response of something, calc will give you the equations (usually something like T1+Ce^(-rt)).
Dave

Jeff,
You already know the answer, so I am not going to answer it but,
I had a similar attitude about calculus when I was struggling with engineering. (Except it took me nearly ten years, and a very wise calculus professor to help me to get over it) I had already taken calculus and dropped out twice, even changing to business because I didn't think I could hack it. I really knew engineering was where I wanted to be, so I gave it one more chance at a junior college calculus night class. I brought this exact issue up one night after class. My professor had spent a majority of his career during the pre-calculator 50's & 60's working in aerospace. With warehouse size rooms full of engineers doing hand calcs for the space program etc... This is what he said: "The reason you need to learn this stuff, (instead of just the formulas/shortcuts) is that you need to be able to recognize when the answers are way off, and the reason it needs to be taught, is that someone needs to be around to teach it again and again. Otherwise it just gets lost. (sadly a fundamental reason CAD software is lacking/unstable at times, is because many of the programmers have such a poor grasp of the theoretical calculus that underlies the complex surfacing)
That late night conversation altered my understanding, and had a "significant" impact on my educational perspective. (and my grades)
I made it through the class, with only a C, but I got an A in math self confidence. And I learned a tremendous set of work & study habits. You can't FAKE it/cram through MATH, like you can with other subjects. You want to know the secret to Math? Do the homework! Do every single problem, assigned or otherwise, whether you know what you are doing or not. DO NOT skip the easy steps! Do the extra credit problems. Do the end of chapter sample tests. If you are willing to put the time into it, it will pay off. It will also have a tremendous impact on your other engineering classes. Especially when you get to Dynamics (which is another class you can't fake)
The very best engineers I have had the pleasure of working with, knew the formulas by heart, because they had worked with them over and over again.
Btw, I aced each and every calculus class I took after that. Statistics, well.. that was a different story altogether.
clay
Jeff Qu> I'm a second year ME student at Oregon State University and I love the

Actually yes.
In my last year as an ME undergrad I was employed as a co-op, watching a recently minted engineer try to determine the required fill volume of grease in a CVJ boot, based off a drawing and a target 'fill line'. One option under consideration was fill a part with a known quantity of grease and spin it up then look to see if the 'fill line' was where it should have been. Then repeat as necessary with different fill volumes.
I sugested he try something called the "Pappus Theorem", which could be found in a calculus text.
Now I get co-ops working for me often and make a point of having them do some "real calculus" in their engineering projects.
Rory
Jeff Qu> I'm a second year ME student at Oregon State University and I love the

I have three words for you
"Castigliano"
It is the way that I do deflections and stresses of flat springs. you have to take the partial derivative of strain energy with respect to a force at the point at which you wish to know the deflection. The strain energy is determined by integrating over the volume of the part in question. I will set up the integral, do the derivative, and then put the result into Excel so that I can optimize using solver.
Chris Stratford, P.E.
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