Green's Theorem is named after the self-taught English scientist George Green (1793-1841). He worked fulltime in his father's bakery from the age of nine and taught himself mathematics from library books. In 1828 he published privately An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism, but only 100 copies were printed and most of those went to his friends.
This pamphlet contained a theorem that is equivalent to what we know as Green's Theorem, but it didn't become widely known at that time. Finally, at age 40, Green entered Cambrigde University as an undergraduate but died four years after graduation. In 1846 William Thompson (Lord Kelvin) located a copy of Green's essay, realized its significance, and had it reprinted.
Green was the first person to try to formulate a mathematical theory of electricity and magnetism. His work was the basis for the subsequent electromagnetic theories of Thomson, Stokes, Rayleigh and Maxwell.
‘The fundamental significance of the vector derivative is revealed by Stokes’ theorem. Incidentally, I think the only virtue of attaching Stokes’ name to the theory is brevity and custom. His only role in originating the theorem was setting it as a problem in a Cambridge exam after learning about it in a letter from Kelvin. He may, however, have been the first person to demonstrate that he did not fully understand the theorem in a published article: where he made the blunder of assuming that the double cross product vanishes for any vector-valued function v = v(x)’.
Green's Theorem is a mathematical theorem that relates the line integral of a two-dimensional vector field over a simple closed curve to a double integral over the region enclosed by the curve.
Green's Theorem was discovered by British mathematician George Green in the 1830s. It was first published in his paper "An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism".
Green was inspired by the work of French mathematician Joseph-Louis Lagrange, who had developed a similar theorem for three-dimensional vector fields. Green extended this concept to two dimensions and developed his own theorem.
Green's Theorem has been used in various fields such as physics, engineering, and fluid mechanics to calculate line integrals and solve problems involving surface and volume integrals. It has also been applied in the study of electric and magnetic fields and in the development of computer graphics algorithms.
Yes, there are several variations and extensions of Green's Theorem, such as the Kelvin-Stokes Theorem, which is a higher-dimensional generalization of Green's Theorem. Other variations include the Divergence Theorem and the Cauchy-Riemann equations, which are used in complex analysis.