What is Stokes’ theorem?
Stokes’ theorem and the generalized form of this theorem are fundamental in determining the line integral of some particular curve and evaluating a bounded surface’s curl. Generally, this theorem is used in physics, particularly in electromagnetism.
What are the applications of Stokes’theorem?
Stokes Theorem Applications. Stokes’ theorem provides a relationship between line integrals and surface integrals. Based on our convenience, one can compute one integral in terms of the other. Stokes’ theorem is also used in evaluating the curl of a vector field. Stokes’ theorem and the generalized form of this theorem are fundamental in
Where did Stokes’theorem come from?
This modern form of Stokes’ theorem is a vast generalization of a classical result that Lord Kelvin communicated to George Stokes in a letter dated July 2, 1850. Stokes set the theorem as a question on the 1854 Smith’s Prize exam, which led to the result bearing his name.
Did George Gabriel Stokes or William Thomson publish the Kelvin Theorem?
The Correspondence between Sir George Gabriel Stokes and Sir William Thomson, Baron Kelvin of Largs, Volume 1: 1846–1869. Cambridge, England: Cambridge University Press. pp. 96–97. ISBN 9780521328319. Neither Thomson nor Stokes published a proof of the theorem. The first published proof appeared in 1861 in: Hankel, Hermann (1861).
What is Stokes’theorem in one sentence?
The classical Stokes’ theorem can be stated in one sentence: The line integral of a vector field over a loop is equal to the flux of its curl through the enclosed surface. Stokes’ theorem is a special case of the generalized Stokes’ theorem.
What is Kelvin Stokes’theorem?
Stokes’ theorem. It was first published by Hermann Hankel in 1861. This classical Kelvin–Stokes theorem relates the surface integral of the curl of a vector field F over a surface in Euclidean three-space to the line integral of the vector field over its boundary: Let γ: [a, b] → R2 be a piecewise smooth Jordan plane curve.