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?