How do Physicists apply Vector Calculus to Physics?

[saminator910]

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.

 

[lurflurf]

The introductory vector calculus is more used by scientists and engineers than mathematicians. There are ways to take many measurements of fluxes. Any book on science or engineering should show how the basic equations are derived. Often it is impractical to measure thousands of fluxes, and a macroscopic balance can be used as a more simple and practical approximation. This may be of interest
http://www.phy.bris.ac.uk/people/berry_mv/the_papers/Berry424.pdf

 

[Square]

Just to pick one example, in classical electromagnetism (the kind that's taught in the first electromagnetism courses on universities) relies heavily on vector calculus . You calculate all sorts of line- and flux integrals over magnetic and electric fields particular while using Maxwells equations.

 

[saminator910]

This may be of interest
http://www.phy.bris.ac.uk/people/berry_mv/the_papers/Berry424.pdf

Hahaha, that's amazing! I never knew one could take the surface integral of a horse. Yes mathematics can have very unexpected applications.