sol3 - Math 264: Advanced Calculus Winter 2008 Assignment 3...

Info iconThis preview shows pages 1–2. 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 264: Advanced Calculus Winter 2008 Assignment 3 Solutions Problem 1 (Adams, 16.2 # 14). Verify the identity ( f ( g h )) = f ( g h ) for smooth functions f,g and h . Solution: We shall use properties stated in Theorem 3 on page 859 in Adams. By the property (b), we have ( f ( g h )) = f ( g h ) + f ( g h ) . By the property (d), the last term can be rewritten as f [ g ) h- g ( h )] = , where in the last equality we have used the property (h) in Theorem 3 in Adams. The result follows. Problem 2 (Adams, 16.3 # 4). Evaluate Z C x 2 y dx- xy 2 dy, where C is the clockwise boundary of the region 0 y 9- x 2 . Solution: Denote the region by R . By Greens theorem (note that the boundary is negatively oriented!) the boundary integral is equal to- Z Z R x (- xy 2 )- y ( x 2 y ) dxdy = Z Z R ( x 2 + y 2 ) dxdy. In polar coordinates, we get Z 3 r =0 Z =0 r 2 rdrd = Z 3 r 3 dr = 81 4 ....
View Full Document

Page1 / 3

sol3 - Math 264: Advanced Calculus Winter 2008 Assignment 3...

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

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