Undergrad A question about Vector Analysis problems

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Finding challenging vector analysis problems, particularly related to Green's, Stokes', and Gauss' theorems, is difficult due to the elementary nature of most exercises in calculus textbooks. These problems are designed to ensure mastery of fundamental concepts before progressing to more complex topics in differential geometry, measure theory, or topology. The formulation of new and interesting problems in vector analysis is challenging, as they require a deep understanding of the subject. Additionally, the perception of what constitutes a challenging problem can vary significantly among individuals. Ultimately, the focus on foundational skills may limit the availability of more advanced problems in standard calculus resources.
flamengo
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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?
 
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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.
 

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