I'm a second year ME student at Oregon State University and I love the
vectors, physics, ProE, etc. classes but Integral Calculus seems like
a giant game. On exams we are forbidden from using calculators or any
small 3x5 notecards to put integrals and differentials on, ick!! I
guess the idea is to make it impossible to have a calculator do the
calculus for you, but it seems ironic in a way to do the job of the
In the engineering specific classes like Statics, for example, we are
allowed calculators and a page of notes on exams. I guess the point
of that is in the engineering world, professional fidelity is not
about remembering math identities by heart, but knowing where to find
them and how to use them,how to verify answers, etc. so as to know for
sure that something will not fall apart when built.
So yeah, how many of you actually calculate integrals out on the job
when you are on the company's time? (I already know the answer to
this, ha ha.)
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
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: email@example.com (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.
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.
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.
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
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?
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
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)).
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
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
Btw, I aced each and every calculus class I took after that.
Statistics, well.. that was a different story altogether.
Jeff Qu> I'm a second year ME student at Oregon State University and I love the
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.
Jeff Qu> I'm a second year ME student at Oregon State University and I love the
I have three words for you
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.
"David T. Croft, Ph.D." wrote in