{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

l_notes07

# l_notes07 - Lecture VII Paths and Curves First we go...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture VII Paths and Curves First we go through several basic notions about paths. Let R ( t ) on [ a, b ] be a given path. Definition 1 R ( t ) is called elementary if for every pair ( t 1 , t 2 ) , with t 1 and t 2 distinct in [ a, b ] , R ( t 1 ) = R ( t 2 ) . Definition 2 R ( t ) is called simple if for every pair ( t 1 , t 2 ) , with t 1 and t 2 distinct in [ a, b ] , except possibly for the pair ( a, b ) , R ( t 1 ) = R ( t 2 ) . R ( a ) = R ( b ) . Definition 3 R ( t ) is called closed if A closed and simple path is called a loop . A loop in E 2 is called a Jordan curve . Given a Jordan curve C , E 2 can be divided into three regions, two bounded and one unbounded. The bounded regions are C and R i , the interior of C . The unbounded region is R e , the exterior of C . Definition 4 A directed curve is a curve along which we have specified a di- rection. Given a curve C , finding a path for C lets us apply calculus techniques. If C is R ( t ) = R cos t ˆ i + R sin t ˆ the circle of radius...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

l_notes07 - Lecture VII Paths and Curves First we go...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online