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Tosh5457
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Is it? If so, can you show how? Thanks ![Smile :smile: :smile:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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deluks917 said:It is possible, what have you attempted?
Tosh5457 said:I don't know where to start, unfortunately the mathematics disciplines in physics, in my university, are a bit superficial, with no theoretical exercises (only exercises to apply the theory). So I'm not trained for this, I want to see someone doing it so I can learn![]()
Tosh5457 said:I'm referring to the Kelvin-Stokes theorem
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The Divergence Theorem and Stokes Theorem are two important theorems in vector calculus that relate the flux (flow) of a vector field through a surface to the divergence (spreading) of the field and the circulation (tendency to rotate) of the field along a boundary curve.
Yes, the Divergence Theorem can be derived from Stokes Theorem by using a special case of Stokes Theorem known as the Kelvin-Stokes Theorem. This special case allows for the use of a surface that is bounded by a single closed curve, which is the case for the Divergence Theorem.
The Divergence Theorem can be written as ∫∫(F · dA) = ∫∫∫(∇ · F) dV, where F is a vector field, dA is an infinitesimal element of surface area, and dV is an infinitesimal element of volume.
The Divergence Theorem is commonly used in fluid mechanics to relate the flux of a velocity field through a surface to the divergence of the field. This allows for the calculation of the net flow of a fluid through a surface.
Yes, the Divergence Theorem and Stokes Theorem have many real-world applications in fields such as physics, engineering, and fluid mechanics. They are used to analyze and solve problems related to fluid flow, electromagnetism, and heat transfer, among others.