{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 265L25 - LESSON 25 Divergence and the Divergence Theorem...

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

LESSON 25 Divergence and the Divergence Theorem READ: Section 18.3 NOTES: The divergence of the vector field -→ F = F 1 -→ ı + F 2 -→ + F 3 -→ k is defined to be div -→ F = ∂F 1 ∂x + ∂F 2 ∂y + ∂F 3 ∂z Example : If -→ F = xe y -→ i + xyz -→ j + sin yz -→ k then div -→ F = e y + xz + y cos yz . Notice that the divergence is a scalar field; that is, vectors are plugged in and numbers are produced. The divergence shows some of the features of ordinary derivatives. For example, it is linear . That is, div a -→ F + b -→ G = a div -→ F + b div -→ G, It also obeys a law reminiscent of the product rule for derivatives. Let -→ F = ρ -→ V be the flux density of a flowing fluid. The vector -→ F ( x, y, z ) points in the direction of the velocity, and its magnitude has units such as grams per square meter per second. In other words, -→ F ( x, y, z ) tells us how much mass of fluid (3 grams say) is flowing in the direction of -→ V ( x, y, z ) at the point ( x, y, z ) per square meter per second. Now imagine a little rectangular box of the fluid, with one corner of the box at ( x, y, z ), and with side lengths given by Δ x , Δ y , and Δ z . We want to compute the mass of the fluid flowing through one face of the box (having (

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

265L25 - LESSON 25 Divergence and the Divergence Theorem...

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

View Full Document
Ask a homework question - tutors are online