1

I am trying to understand the difference between multivariate calculus and Vector calculus. If it's mentioned f(x,y) = xy, is it a multivariate or the x,y can be considered as vector and therefore, its a vector calculus and gradient will be calculated?

Quoting from the https://arxiv.org/pdf/1802.01528.pdf "To make it clear we are doing vector calculus and not just multivariate calculus, let’s consider what we do with the partial derivatives"

Note: I went through this link also link

and it says"Calc 3 = multivariable calculus = vector analysis. A semester mostly working on partial derivatives, surface integrals, stuff like that. Introduction of Stokes and Green's thereoms". If there is a function f(x,y), it's not necessary that x,y are vectors?so, this is multivariate calculus?

user13034532
  • 21
  • 1
    Multivariable - when domain of functions have more one dimension, vector - when range. – zkutch Aug 05 '23 at 09:24
  • 2
    They are roughly interchangeable, but it probably varies by region. In my mind multivariable calculus extends calculus to its full capacity when the domain and range can have dimension $\ge 1$. Vector calculus applies that to vector fields. But vectors in $\Bbb R^3$ are just points in $\Bbb R^3$ with a fancy name, so until you need to worry about more general manifolds or infinite dimensional vector fields, I don't think it matters a ton. – pancini Aug 05 '23 at 09:44

0 Answers0