This lecture discusses Green's theorem in the plane. Green's theorem not only gives a relationship between double integrals and line integrals, but it also gives a relationship between "curl" and "circulation". In addition, Gauss' divergence theorem in the plane is also discussed, which gives the relationship between divergence and flux.
This is a series of lectures for MATH2111 "Higher Several Variable Calculus" and "Vector Calculus", which is a 2nd-year mathematics subject taught at UNSW, Sydney. This playlist provides a shapshot of some lectures presented in Session 1, 2009. These lectures focus on presenting vector calculus in an applied and engineering context, while maintaining mathematical rigour. Thus, this playlist may be useful to students of mathematics, but also to those of engineering, physics and the applied sciences. There is an emphasis on examples and also on proofs.
Founded in 1849, the University of New South Wales (UNSW) is one of the world's leading research universities and part of the Universitas 21, a coalition of international research-focused universities. As one of Australia's leading schools, its campuses teach over 46,000 students in 600 academic programs. In 2009, the Financial Times ranked UNSW's The Australian School of Business the top MBA program in Australia and 32nd in the world. During the school's relatively short history, it has also managed to produce some of the leading political figures in Australia including a foreign minister in Bob Carr and former Attorney General of Australia, Robert McClelland.