PS4_answers - ( , ) ( x,y ) = ( x- ) 2-( y- ) 2 . A6. u xx...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Here are answers to most of the problems. I have, of course, not included ones in which the question asks to prove or verify something. Also, for now, I have not had a chance to include pictures. Math 237 Problem Set 4 Answers A1. a) Hf (2 , 3) = ± 9 - 6 - 6 4 ² . b) L a (2 , 3) = f (2 , 3) + f x (2 , 3)( x - 2) + f y (2 , 3)( y - 3) = 1 + 3( x - 2) - 2( y - 3). P 2 , (2 , 3) ( x,y ) = 1 + 3( x - 2) - 2( y - 3) + 9 2 ( x - 2) 2 - 6( x - 2)( y - 3) + 2( y - 3) 2 c) The level curves of f are straight lines. A2. i) P 2 , (1 , 0) ( x,y ) = ln 2 + 1 2 ( x - 1) + 1 2 y - 1 8 ( x - 1) 2 - 1 4 ( x - 1) y + 1 8 y 2 . ii) P 2 , (1 , 1) ( x,y ) = 1 + 2( x - 1) - ( y - 1) - 3 2 ( x - 1) 2 - 2( x - 1)( y - 1) + ( y - 1) 2 A3. P 2 ,
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ( , ) ( x,y ) = ( x- ) 2-( y- ) 2 . A6. u xx + u yy = D 2 1 f + D 2 2 f , u xx-u yy = D 2 1 f cos 2 -D 1 D 2 f sin 2 -D 2 D 1 f sin 2 -D 2 2 f cos 2 . u xy = 1 2 D 2 1 f sin 2 -D 1 D 2 sin 2 + D 2 D 1 cos 2 -1 2 D 2 2 f sin 2 . B1. The only function is f ( x,y ) = 1 2 x 2 + 2 xy-3 2 y 2-3 x + 3 y + 19 2 . B2. b) c , c) u ( x,t ) = Ae-( x + ct ) 2 1...
View Full Document

This note was uploaded on 11/30/2010 for the course MATH 235/237 taught by Professor Wilkie during the Spring '10 term at Waterloo.

Ask a homework question - tutors are online