Conditions required for simply connected regions

Description
Validity of the Green's theorem is analysed in various conditions. This theorem is applicable when the vector field is defined completely. The condition required for a connected region R to be simply connected is explained.Application of this theorem is shown through examples.
Prof. Denis Auroux, Maths, Fall 2007,18.02 Multivariable Calculus: 24: Simply Connected Regions, Massachusetts Institute of Technology: MIT OpenCourseWare),http://ocw.mit.edu (Accessed September 28,2011). License: Creative Commons BY-NC-SA:http://ocw.mit.edu/terms/#cc