A question about Vector Analysis problems

[flamengo]

Why is it difficult to find really challenging vector analysis problems (problems about Green's, Stokes' and Gauss' theorems in a Calculus 3 course) in Calculus books? Most of the problems are elementary, at least that's the impression I have(I could be wrong). Is it really difficult to formulate new and interesting problems in this part(Vector Analysis), or do the authors try to go very slowly on this part of the subject?

 

[fresh_42]

Stokes (and its many variations) is one of the deepest results in mathematics at all. It cannot be left out. The problems are elementary because they have to be well practiced and known in sleep, before one can turn to more complex examples in differential geometry, measure theory or topology. And challenging is a very individual attribute.