# s10wk11 - Math 23 B Dodson Week 10 Homework[due April 16...

This preview shows pages 1–3. 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: Math 23 B. Dodson Week 10 Homework: [due April 16] 16.1, 16.2 vector fields and line integrals 16.3 Fundamental Theorem for line integrals 16.4 Green’s Formula Problem 16.1.26. Find and sketch the gradient field of f ( x, y ) = 1 2 ( x + y ) 2 . Solution. The gradient field-→ ∇ f = < f x , f y >, so f x = 1 2 · 2( x + y ) = x + y, and f y = 1 2 · 2( x + y ) = x + y gives-→ ∇ f = < x + y, x + y > . For the sketch, we pick a few values-→ ∇ f (1 , 2) = < 3 , 3 >,-→ ∇ f (1 , 3) = < 4 , 4 >,-→ ∇ f (1 ,- 2) = <- 1 ,- 1 > and draw displacement vectors < 3 , 3 >, < 4 , 4 >, <- 1 ,- 1 > starting at (1 , 2) , (1 , 3) , (1 ,- 2) respectively. Problem 16.2.5: Evaluate the line integral Z C xy dx + ( x- y ) dy, where C is the curve consisting of line segments from (0 , 0) to (2 , 0) and from (2 , 0) to (3 , 2) . 2 Solution: By definition, Z C = Z C 1 + Z C 2 . For C 1 we pick the simplest parameterization x = t, y = 0 for 0 ≤ t ≤ 2 . Then substituting the parameterization,...
View Full Document

{[ snackBarMessage ]}

### Page1 / 5

s10wk11 - Math 23 B Dodson Week 10 Homework[due April 16...

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

View Full Document
Ask a homework question - tutors are online