hw1_sol - Mathematics 20E - Spring 2009 - Homework 1 April...

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Unformatted text preview: Mathematics 20E - Spring 2009 - Homework 1 April 19, 2009 Please complete the following problems and turn them in following the directions that will be announced in class and on the website by Friday, April 10 at 5:30pm. Only a subset of the problems will be graded; leave some blank at your own risk. 1. Compute the total derivative of the following functions. (a) f : R R 2 , f ( x ) = parenleftbigg xe x cos( x 2 ) parenrightbigg Solution : The total derivative will be the 2 1 matrix-valued function given by D f ( x ) = parenleftbigg ( x + 1) e x 2 x sin( x 2 ) ] parenrightbigg (b) g : R 2 R , g ( x ) = x 1 e x 2 + cos( x 1 x 2 ) Solution : The total derivative will be the 1 2 matrix-valued function given by Dg ( x ) = ( e x 2 x 2 sin( x 1 x 2 ) x 1 e x 2 x 1 sin( x 1 x 2 ) ] ) 1 (c) h : R 2 R 2 , f ( x ) = parenleftbigg x 1 e x 2 cos( x 1 x 2 ) parenrightbigg Solution : The total derivative will be the 2 2 matrix-valued function given by D h ( x ) = parenleftbigg e x 2 x 1 e x 2 x 2 sin( x 1 x 2 ) x 1 sin( x 1 x 2 ) ] parenrightbigg 2. Give the linearization of h : R 2 R 2 , f ( x ) = parenleftbigg x 1 e x 2 cos( x 1 x 2 ) parenrightbigg near parenleftbigg 1 parenrightbigg ....
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This note was uploaded on 10/22/2009 for the course CHEM 140A taught by Professor Whiteshell during the Spring '04 term at UCSD.

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hw1_sol - Mathematics 20E - Spring 2009 - Homework 1 April...

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