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The Green’s theorem can be related to which of the following theorems mathematically?
- a)Gauss divergence theorem
- b)Stoke’s theorem
- c)Euler’s theorem
- d)Leibnitz’s theorem
Correct answer is option 'B'. Can you explain this answer?
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The Green’s theorem can be related to which of the following the...
The Green’s theorem is a special case of the Kelvin- Stokes theorem, when applied to a region in the x-y plane. It is a widely used theorem in mathematics and physics.
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The Green’s theorem can be related to which of the following the...
Stoke's Theorem and Green's Theorem Relationship:
Green's theorem and Stoke's theorem are closely related in the field of mathematics. Stoke's theorem is a generalization of Green's theorem in two dimensions to higher dimensions. Both the theorems relate the circulation of a vector field around a closed curve to the flux of the curl of the vector field through the surface enclosed by the curve.
Mathematical Relationship:
- Green's Theorem: In two dimensions, Green's theorem relates a double integral over a region in the xy-plane to a line integral around the boundary of the region.
- Stoke's Theorem: Stoke's theorem generalizes Green's theorem to three dimensions. It relates the surface integral of the curl of a vector field over a surface to the line integral of the vector field around the boundary of the surface.
- Relationship: Stoke's theorem can be seen as an extension of Green's theorem from two dimensions to three dimensions. It provides a way to relate the circulation of a vector field over a closed curve in three dimensions to the flux of the curl of the vector field through the surface enclosed by the curve.
Therefore, the Green's theorem can be mathematically related to Stoke's theorem as an extension of the same concept to higher dimensions.
Green's theorem and Stoke's theorem are closely related in the field of mathematics. Stoke's theorem is a generalization of Green's theorem in two dimensions to higher dimensions. Both the theorems relate the circulation of a vector field around a closed curve to the flux of the curl of the vector field through the surface enclosed by the curve.
Mathematical Relationship:
- Green's Theorem: In two dimensions, Green's theorem relates a double integral over a region in the xy-plane to a line integral around the boundary of the region.
- Stoke's Theorem: Stoke's theorem generalizes Green's theorem to three dimensions. It relates the surface integral of the curl of a vector field over a surface to the line integral of the vector field around the boundary of the surface.
- Relationship: Stoke's theorem can be seen as an extension of Green's theorem from two dimensions to three dimensions. It provides a way to relate the circulation of a vector field over a closed curve in three dimensions to the flux of the curl of the vector field through the surface enclosed by the curve.
Therefore, the Green's theorem can be mathematically related to Stoke's theorem as an extension of the same concept to higher dimensions.
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The Green’s theorem can be related to which of the following theorems mathematically?a)Gauss divergence theoremb)Stoke’s theoremc)Euler’s theoremd)Leibnitz’s theoremCorrect answer is option 'B'. Can you explain this answer?
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