I did the same thing in a biology class ages ago, where part of the assignment was to measure the area of a leaf. Weigh the leaf, weigh a precisely cut area ( or better, various sample square areas) from the leaf, do the math. Surprisingly, the instructor was astounded. He expected people to lay graph paper over the leaf and count squares.
There is a similar story of Edison showing one of his mathematician employees how to measure the volume of a light bulb. Instead of approximations and integrals, he filled an empty bulb with water.
The last industrial use I know of a planimeter was in a leather shop, measuring the before and after area of hides after various processing steps. The more calculus oriented versions were ball and disk integrators used in some mechanical analog computers.
I took the required Calculus courses (and the required foreign language courses!) when I got an EE degree. But I went into software engineering after that and didn't take more than the required Calculus courses. I know there are a few engineers who really think in poles and zeroes and LaPlace transforms, they have a different vocabulary to think with. A bought a book on LaPlace transforms, I know we never covered what's in there. I doubt I'll ever be really comfortable in that domain. Do I NEED that? Apparently not. But I recognize that it's something I could have studied and probably should have if I wanted to pursue a career in electrical engineering, it would have been useful.
I remember a physics lab in which my partner and I created a strip-chart recording that plotted a variable of some sort. Then we had to find the area under the curve. Because this was experimental data and not a function we could describe with an equation, we carefully cut out the "area" under the curve and weighed it on an analytical-type scale. Then we weighed a 10-by-10-cm piece of the same chart paper. After that, the "integration" was simple math.
Well, you could have taken your raw data points and done a Newton-Raphson summation, instead. Just assume the area is an array of rectangles of width equal to the spacing between samples of the independent variable and height equal to the data point.
That being said, learning the Calculus is a great thing for engineering students--even if it is never used, even if it is hard. How far to go is anyone's guess. But exactly how far up the mathematics ladder you choose to go determines your future possibilities. Period.
I'll bet many engineers haven't used much Trigonometry since they found CAD. And I know I haven't even done long division or extracted a single nth-root either. But that's not a reason to avoid learning it.
I can only talk from a UK perspective, where the standard of mathematics of graduates is frequently dangerously low; I'm a Mechanical Engineer.
Much first degree work is aimed at proving a level of intellectual capability- sometimes the actual subject matter is less important. My head of school used to say that the most important thing was that he taught us how to learn.
Many good points have been made about analysis software and so on that may negate the need for the user to understand maths, but unless you know what is behind a piece of software, then you and it in combination may merely be a dangerous weapon, like the FE packages that are attached to CAD systems, in the hands of CAD jockeys and not engineers. After all, we did not stop learning arithmetic on the basis of electronic calculators being introduced.
Not everyone in Engineering will use calculus regularly- or at all- but given that we cannot specialise from day one, then everyone will have to learn a bit of everything.
At my last employer, while recruiting, I expected any Engineering candidate not to be fazed by a simple ordinary diferential equation. I'd allow some book work to brush up, but a designer, stressman, analyst of any kind, reliability engineer and so on ought to be able to appreciate calculus and in most cases to be able to do some calculus, otherwise we're just regurgitating formulae with no idea of their background and limits of application, and are then genuinely dangerous.
Even in Project Management and Quality Engineering, procedures are often drawn from theories with limits, for which calculus is critical, and it can be useful, believe me.
The question is- how far do you go- but no one should be entitled to call themselves a professional engineer without having achieved a reasonable grasp of calculus, algebra, statistics, geometry and no doubt others I've forgotten to list.
What we must do is to engage early with real applications, and show the sheer beauty of mathematics as well as its usefulness.
First, I have been a part of new product development for over 15 years, I have never had to use calculus. Force caluclations? Yes. Complex geometric interactions? Yes. Mixed materials? Yes. Etc... No calc though. I also have no issue with the classes because they do teach you stuff the layman never would understand and that expansion of thinking makes you more an engineer than the CAD jockey who gets promoted.
The issue is does Calculus classes take away from hands on product design engineering learning we all do day in and day out? Industrial designers have to make what they design in classes for 2-3 years, and is about half their classes. What amount of time does the average engineering student spend in his/her undergraduate actually designing, making, and testing their ideas? There is the issue that Calc and other foundation classes have, they take away from what the corporations would like to see from graduates (undergrad degrees), some practical experience...
I agree that, with the sheer volume of material which needs to be covered in four years, it's unrealistic to require science and engineering students to learn a foreign language. But it ought to be strongly encouraged. Being bilingual in English and Spanish has greatly enriched my life, both professionally and personally. (For one thing, I doubt that I would have married my wife, who is from El Salvador, if I didn't speak Spanish). I wish I knew French and German, since I regularly work with colleagues in Quebec and Austria. Of course, most educated people in those places speak English, but if they went to the trouble to learn my language, why shouldn't I do the same? Mandarin Chinese would be a good one to know, too. I've met a number of second-generation Americans who seem to be proud of not knowing their parents' language. This seems to me to be a foolish attitude. The more languages a person can speak, the better.
I know engineering and science majors must take difficult courses, and we all have. But I draw the line at courses that have no practical value in terms of knowledge or techniques. Years ago science and some engineering students had to take a foreign language for 2 or 3 semesters. Supposedly those courses would help the students translate scientific papers from German into English. I took two semesters of German as a sophomore and one more semester as a senior. I used my "knowledge" of German exactly once. At the time a MS in chemistry required passing a translation test, but examinees could use a technical German-English dictionary! I never used German again and can't say I feel constrained without fluency in a spoken language other than English. As far as I know, most colleges and universities have given up foreign language requirements for science and engineering students, although a few might hold on. Students would do better to learn C or LabVIEW.
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