{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

l_notes26

l_notes26 - Lecture XXVI The Divergence Theorem In this...

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

Lecture XXVI The Divergence Theorem In this lecture, we will define a new type of derivative for vector fields on E 3 , called divergence . Let F be a vector field defined on a domain D . Let us start by defining the divergence of F on interior points of D , i.e. points P such that there exists a sphere of center P and radius a > 0 with its interior contained in D . Definition 1 Let F be a continuous vector field on D in E 3 . Let P be an interior point of D , and let S ( P, a ) be the sphere of center P and radius a , for all a > 0 . The volume of S ( P, a ) is 4 πa 3 and the ﬂux of F through S ( P, a ) is 3 F d�σ . Consider the limit S ( P,a ) · 3 lim F d�σ. a 0 4 πa 3 · S ( P,a ) If this limit exists, then it is called the divergence of F at P , and it is denoted by div | P . F Below are two important properties of divergence. F is C 1 on D , then the divergence of 1. Existence: If F exists at every interior point of D .

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.

{[ snackBarMessage ]}

Page1 / 2

l_notes26 - Lecture XXVI The Divergence Theorem In this...

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

View Full Document
Ask a homework question - tutors are online