how do I make difference between vector valued functions and vector fields, I am confused how they differ and how are they same? Which is used with what? What about a function F(x,y,z,t) = (f1(x,y,z,t), f2(x,y,z,t), f3(x,y,z,t)) which maps R4 to R3, what type of function is this? F(x,y) = x^2 + 2y F(x,y,z) = x^2 + y^2 + 10z F(x,y,z,t) = 3x + 2y - z^2 + t F(t) = (t^2 , 0 , t^3) F(x,y) = (x^2 + y, y^2 - x) F(x,y,z) = (z+xy,y^2+z, 2x-z) F(x,y,z,t) = (z-t^2,y^2, xt+z) which of these functions is what type and why? Also what is a potential field. Finally how do they all (vector field, potential field, vector valued function) differ when compared to curve/surface in R3? A short description shall suffice, thanks. Its just that I can't find the answer summarised anywhere making good distinction.