A7 - F G and use the chain rule in matrix form to nd the...

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

View Full Document Right Arrow Icon
Math 237 Assignment 7 Due: Friday, Nov 14th 1. Consider the following maps T : R 2 R 2 . Find the image under T of the rectangle D = { ( x,y ) R 2 | 1 x 3 , 2 y 3 } . a) T ( x,y ) = ( x + y,x - y ). b) T ( x,y ) = ( x cos( πy/ 3) ,x sin( πy/ 3)). c) T ( x,y ) = ( xy,x 2 - y 2 ) 2. Invent a transformation that transforms a) The ellipse x 2 + 6 xy + 10 y 2 = 2 onto the unit circle. b) The disc x 2 + y 2 1 onto the square 0 u 2, 0 v 1. 3. Consider the maps F : R 2 R 2 and G : R 2 R 2 defined by F ( u,v ) = ( e uv ,e u - v ) , G ( x,y ) = ( x 2 + y 2 ,x 2 y 2 ) . a) Calculate the composite map
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: F G and use the chain rule in matrix form to nd the derivative matrix D ( F G ). b) Calculate D ( G F )(1 , 1). 4. Let F : R 2 R 2 be dened by F ( x,y ) = p x 2 + y 2 , x x 2 + y 2 . Use the linear approximation of mappings to nd the approximate image of the point (3 . 1 , 3 . 9) under F ....
View Full Document

This note was uploaded on 04/18/2010 for the course MATH 237 taught by Professor Wolczuk during the Spring '08 term at Waterloo.

Ask a homework question - tutors are online