I'm trying to finish reading/understanding the textbook we used in Calculus III (multivariate), as we only covered chapters 12-18, but I'm stuck on something. We used McCallum/Hughes-Hallett/Gleason, and I'm referring to section 19.3 (if you have the text) which is about flux integrals over parameterized surfaces. I actually feel strong about my understanding of the flux integral itself using the sum of dot products of the vector field at a location and the area vector generated by a cross product of the partials at that location over the surface, but I need help understanding/visualizing the parameterization of a surface. I understand how to parameterize a curve in 3-space based on time, but how do you parameterize a surface based on two variables, and visualize this? I can visualize a point drawing a line as t is changed, but the text includes no preface to this section regarding the parameterization of surfaces. Say x, y, and z are dependent upon the two variables s and t. For a line I visualize t as being time, but what would s be when parameterizing a surface? Does anyone have any tips or articles they could point out? Thanks.