# What would be a good pacing for teaching this calculus 2 course?

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?

• 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. Commented Oct 6, 2023 at 17:40
• That's pretty much Calc III where I worked (except that sequences and series is in Calc II). Commented Oct 6, 2023 at 19:03
• 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? Commented Oct 6, 2023 at 20:24
• @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. Commented Oct 6, 2023 at 22:19
• 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. Commented Oct 7, 2023 at 1:38