Question

what may be d possible course structure for 1st year undergrad in vector calculus for math?

Answer 1

Usually covered in: some colleges call it Cal III, others call it multivariable calculus.

Answer 2

mainly start with revision of basic vectors ( dot products, cross products etc )

Answer 3

then they introduce "vector functions", which are pretty similar to normal functions

Answer 4

then they do basic revision of differentiation in one dimension and then extend that to vector functions

Answer 5

learn lagrange multipliers , a method of optimisation of functions of several variables and learn about directional derivatives

Answer 6

then they do basic revision of one dimensional integrals, and extend that to functions of more than one variable , introduce double integrals and the various ways of evaluating them

Answer 7

then you learn a bit about some physics concepts, "work" and "flux" etc ,