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In our university both math and engineering students attend in the same calculus classes. There are arguments in our department about the possible influences of this approach on students. It seems based on the students' needs in their future career they need different types of calculus. For example in a calculus class for the math students, the teacher should emphasize on the abstract aspects, proofs, generalizations and the interactions with the other fields of mathematics and in a calculus class for engineering students, the applications and calculation are more important features of the course.

Question. Is there any difference in teaching calculus for the math and engineering students? Should math and engineering students attend in separated calculus classes?

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One might also argue that engineering graduates should be able to perform rigorous mathematical proofs in calculus even though that is not a major vocational skill for them. If the engineering department does argue that, then it makes perfect sense to share the course with the mathematicians, the argument for a different emphasis disappears. So maybe the departments should independently describe their preferred calculus syllabus. The similarities/differences between the two will help tell you whether the students should be in the same class, and how much compromise is needed if so. –  Steve Jessop Mar 27 at 11:58

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In my understanding, multiple representations of a concept benefit conceptual understanding. Hopefully the differences among departments can be negotiated to benefit students. Maybe a question to discuss is how we differentiate instruction for diverse learners in a single classroom. After all, even in a pure mathematics classroom all learners are at different places with their prior knowledge and different potential for learning. So philosophically and in my opinion having students from engineering and mathematics (and physics, if you like) in the same classroom can benefit both groups. It does require competent teacher to be able to handle such class.

I do recognize significance of different contexts and different opinions, so, in reality some negotiations between departments have to happen.

A paper that might be of interest:

Dunn, J. W., & Barbanel, J. (2000). One model for an integrated math/physics course focusing on electricity and magnetism and related calculus topics. American Journal of Physics, 68(8), 749-757.

Some references (although mostly focused on k-12) in support of this kind of thinking:

  1. Ellis, E., Gable, R. A., Gregg, M., & Rock, M. L. (2008). REACH: A framework for differentiating classroom instruction. Preventing School Failure, 52(2), 31-47.
  2. Nunley, K. (2004). Layered curriculum (2nd ed.). Amherst, NH: Brains.org
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Mara, Thank you very much for your interesting answer and useful references. –  Saint Georg Mar 29 at 8:21

Tentatively, yes.

In the universities I've taught, there are substantial differences between those courses:

For engineering students, the courses in calculus (and linear algebra) provide some supplemental, rather abstract information which helps to understand the techniques taught in other classes, such as mechanics and electrodynamics. This is why I think that a good calculus course for engineering students has a curriculum which is coordinated with the engineering classes, uses a lot of examples from those subjects and is light on hard proofs (uses motivations and rough explanations instead).

Calculus for mathematicians is a main subject on its own; it should be thorough and you can afford not to be in tune with some other classes which cover related subjects. Proofs should be precise, but examples can still help to understand the theorems.

It's worth noting that students of physics deserve their own calculus curriculum as well due the use of more advanced tools in modern theoretical physics compared to the engineering classes.

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There is a danger that lies in tailoring a class too much towards a major and it is that it won't broaden the students' worldviews. What follows a calculus course is years of specialization. Why start early when the students will see all this stuff anyway in their degree? Take an engineer for example. They'll be doing engineering and speaking with their engineering peers and professors for several years. A more abstract calculus course can be a great opportunity to build strong foundations for those engineering students and this can only help them later on.

This doesn't mean there shouldn't be an tailoring towards particular fields. More so, I believe that calculus courses should be taught the same way regardless of specializations. Teach everyone rigorously (as possible for such a level) and introduce examples from various fields. Most of the biology, business or engineering students I've tutored suffer from poor understanding of the fundamental calculus concepts and not of how they apply to their field. Once we cover those basics they usually have no problem with the applications.

Perhaps the ideal homework would contain enough abstract examples to teach the concepts, followed by problems from various fields with an emphasis on the students' specialization.

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Sure. For example, engineers don't mess with fields apart from the real numbers. They only mess with quite particular Hilbert spaces. They don't mess with Galois fields apart from GF(2) in communication and coding theory. They don't work quaternions or generally non-commutative groups.

They'll not even learn the tools for computational analysis (like generating functions and everything around them). If they do use generating functions, their variable is called $z^{-1}$. If they use Fourier transforms, their domain variable is called $2\pi f$. When they work with integral transforms, convergence is assumed. They learn the formulas for main tension values, main inertial axes, and transformations of quadratic forms separately.

Number theory is not covered, tensors are mostly left to the physicists to play with.

For three-phase electric systems, they have transforms used for diagonalizing circular impendance matrices without recognizing those transforms as a 3-point DFT.

In general, a lot of stuff is learnt multiple times under separate names, with separate scaling and naming constants and sign conventions.

Proofs are not really all that important. It's more important for the engineers to be able to apply mathematical tools rather than to create them: a carpenter only needs rather limited knowledge of plant biology.

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How does this affect calculus classes? That was the question. –  Matt F. Mar 27 at 17:36

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