{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Green's Theorem Power Point Notes

# Green's Theorem Power Point Notes - applied to every line...

This preview shows pages 1–3. Sign up to view the full content.

Slide 1 Calculus III Section 14.4 Green’s Theorem Slide 2 Definitions A curve is simple if it does not cross itself. A region is simply connected if its boundary is one simple closed curve. Examples Slide 3 Green’s Theorem Let R be a simply connected region with a piecewise smooth boundary C, oriented counterclockwise (that is, C is traversed once so that the region R always lies to the left ). If M and N have continuous partial derivatives in an open region containing R, then ∫∫ - = + C R dA y M x N Ndy Mdx

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

View Full Document
Slide 4 Example 14.4, #10 Note:
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: applied to every line integral. However, when it does apply it can save time. Slide 5 Line Integral for Area If R is a plane region bounded by a piecewise smooth simple closed curve C, oriented counterclockwise, then the area of R is given by ydx xdy A C-= ∫ 2 1 Slide 6 Example 14.4, #25 Slide 7 Vector Forms of Green’s Theorem ( 29 ∫∫ ∫∫ ∫ • = ∂ ∂-∂ ∂ = + R R C dA k F curl dA y M x N dy N dx M dA F div ds N F R C ∫∫ ∫ = •...
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

Green's Theorem Power Point Notes - applied to every line...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online