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Next semester I'm going to lecture calculus 2 in an institution I just joined. However, when I had calculus 2 back then the syllabus was very different, it mainly covered several variable calculus up until derivatives, including all that analysis of implicit/inverse function theorem, Lagrangian multiplier method, and so on...

For this course, on the other hand, the syllabus goes more or less like this:

  • Functions of several variables
  • Partial derivatives, directional derivatives and gradients
  • Integrals of functions of several variables
  • Sequences and series of functions
  • Line integrals, Green's theorem, rotational and divergent
  • Surface integrals, Stokes' and Gauss' theorem

I remember having the functions of several variables and differentiability parts in Calculus $2$, then line and multivariate integrals in Calculus $3$, and then sequences and series part was in another course still (I majored in mathematics). This is a one-semester course for engineering, so I take it the course should not be aimed at analyzing things as thoroughly, but still it seems kind of an all-over-the-place syllabus to organize... How would you go on organizing this course? What would you focus more on? Would it be wise to separate in 3 big parts as "limits/differentiability then sequences/series and then line/surface integrals"? Or would you do it differently?

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    $\begingroup$ Do you have a standardized textbook? Most standard books are structured that the sections take up roughly equal time, and usually come with premade slideshows to support that. No need to reinvent the wheel. $\endgroup$ Commented Oct 6, 2023 at 17:40
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    $\begingroup$ That's pretty much Calc III where I worked (except that sequences and series is in Calc II). $\endgroup$
    – Sue VanHattum
    Commented Oct 6, 2023 at 19:03
  • $\begingroup$ How many credits, or contact hours per week? Is this US semester system, or quarter system or something else? And how much is covered in the prerequisite Calc 1? $\endgroup$
    – user52817
    Commented Oct 6, 2023 at 20:24
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    $\begingroup$ @karlabos Thanks, this is helpful. A typical calculus class might be 4 or 5 contact hours per week for 15 weeks, so 60-75 hours total, compared to your 102 hours. I suspect the same is true for Calc 1, so includes much more content that a more typical Calc 1 course. $\endgroup$
    – user52817
    Commented Oct 6, 2023 at 22:19
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    $\begingroup$ I agree with @DanielR.Collins . Get a good textbook, and follow it closely. [Perhaps the same textbook used the last time the course was offered.] Do not add your own tweaks. Do not add your own notation. $\endgroup$ Commented Oct 7, 2023 at 1:38

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In the US, most of both of your variants is covered in 3rd semester calc. A bit of a drive by of the different topics given the number of them and the differences if them. Still manageable with tailored difficulty books. But the students tend to get exposure more than mastery. In a way that is different from their experience in single variable calculus. Sequences and series are usually a week or so within 2nd semester calc...and are a bit off the main theme, tacked on at end.

Looking at it practically, you seem to have a text and pacing for the bulk of yhe course. Just need to squeeze in series stuff. My advice is do a week on it, no more. It is really just another exposure. No...don't use that book that you have. Will be too long and need too much tailoring. Instead look at a typical us calc book like Thomas or Stewart. Either will have a week long capsule.

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  • $\begingroup$ These days there are plenty of excellent "typical US calc books" available for free on the internet; I recommend choosing one of them rather than make students pay for the material. $\endgroup$ Commented Oct 7, 2023 at 4:40
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    $\begingroup$ Yeah, sure. Was never suggesting to make whole class buy texts for one chapter, one week, anyhow. Just the teach here to buy or better yet look at a few to see the coverage. They are pretty cheap on amazon for used copies if he doesn't have library access. And probably worth having as a professional just to see how the cat is skinned. $\endgroup$ Commented Oct 7, 2023 at 9:41
  • $\begingroup$ Fwiw, i often see online free texts recommended on stack, not surprising given the computer slant of people here...we also get the TEX pushers for similar reasons. But I've been mostly underwhelmed by the quality of free texts in terms of editing, problems, typography, etc. $\endgroup$ Commented Oct 7, 2023 at 9:44
  • $\begingroup$ Give these online calculus texts a look. They're also mobile-friendly which is a desirable feature to students. $\endgroup$ Commented Oct 7, 2023 at 18:18

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