Green's theorem and Jordan theorem.

Description
A region on a plane is described. For a open set in a plane bounded by a simple closed piece-wise -differentiable curve, the Green's region is defined and hereby Green's theorem is stated and analysed. The condition under which a continuously differentiable vector field, defined in an open set is said to be a gradient of a vector field are discussed in this lecture note by Prof. James Munkres. Jordan curve theorem for stairstep curve is stated and proved.
Prof. James McKernan, Maths, 18.024. Calculus with Theory II, Spring 2003: Green's theorem and its application: Massachusetts Institute of Technology: MIT OpenCourseWare),http://ocw.mit.edu (Accessed October 24, 2011). License: Creative Commons BY-NC-SA:http://ocw.mit.edu/terms/#cc