So, how do people, like physicists, or engineers, actually apply the concepts of vector calculus to their work. For example, if they want to calculate flux or something they need a vector field, how do they approximate that vector field? are their specific equations that can approximate vector fields for flow over objects such as airplane wings, or flow through a pipe? Honestly I'm more of a math person, and this has perplexed me since I started learning about calculus in general, how do people who apply derivatives and integrals derive the equations they are doing them on? Are most well known and established, such as simple ones like d=.5at^2 + vit for trajectory? I don't really know if this belongs in the math section but oh well.