MAT 213 Lecture Notes - Lecture 28: Curve, Open Set, Simply Connected Space
Document Summary
Provide a generalization to each of the key terms listed in this section. So, if you let both p and q be (continuous) partial derivatives while they"re on an open region that has d (a bounded region), then the following would be created: Sometimes, the following can be used (based on however you were taught green"s theorem) when it comes to a line integral that"s calculated thanks on the positive-orientation of c (a closed curve): Since d is considered to be the positive-oriented boundary curve of d, then the following can be expressed thanks to green"s theorem: The "positive orientation" of c (a simple, closed curve) deals with c"s (a simple, closed curve"s) single counterclockwise traversal. If you really do think about it, green"s theorem can actually be references as a "counterpart" of the fundamental theorem of calculus when it comes to the double integrals. 2nd part to the fundamental theorem of calculus:
