8/18/2023 0 Comments Surface integral formula![]() ![]() Cauchy (1846) "Sur les intégrales qui s'étendent à tous les points d'une courbe fermée" (On integrals that extend over all of the points of a closed curve), Comptes rendus, 23: 251–255. In 1846, the form of "Green's theorem" which appears in this article was first published, without proof, in an article by Augustin Cauchy: A. Green did not actually derive the form of "Green's theorem" which appears in this article rather, he derived a form of the "divergence theorem", which appears on pages 10–12 of his Essay. ![]() ^ George Green, An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism (Nottingham, England: T.Reading, Massachusetts, U.S.A.: Addison-Wesley Publishing Company, INC. Mathematical Methods for Physics and Engineering. Shoelace formula – A special case of Green's theorem for simple polygons.Method of image charges – A method used in electrostatics that takes advantage of the uniqueness theorem (derived from Green's theorem).Bernhard Riemann gave the first proof of Green's theorem in his doctoral dissertation on the theory of functions of a complex variable. This is in fact the first printed version of Green's theorem in the form appearing in modern textbooks. In 1846, Augustin-Louis Cauchy published a paper stating Green's theorem as the penultimate sentence. It is named after George Green, who stated a similar result in an 1828 paper titled An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism. Lemma 1 (Decomposition Lemma) - Assume Γ History ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |