s11wk11su

s11wk11su - Math 23 B. Dodson Week 5b Homework: 16.1, 16.2...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 23 B. Dodson Week 5b Homework: 16.1, 16.2 vector fields and line integrals 16.3 Fundamental Theorem for line integrals 16.4 Greens 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 integraldisplay 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, integraldisplay C = integraldisplay C 1 + integraldisplay C 2 . For C 1 we pick the simplest parameterization x = t, y = 0 for 0 t 2 . Then substituting the parameterization, xy = 0 , so integraldisplay C...
View Full Document

Page1 / 5

s11wk11su - Math 23 B. Dodson Week 5b Homework: 16.1, 16.2...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online