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Homework-8-f10_Sol

# Homework-8-f10_Sol - AMS 361 Applied Calculus IV by Prof Y...

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1 AMS 361: Applied Calculus IV by Prof Y. Deng Homework 8 Assignment Date: Tuesday (11/09/2010) Collection Date: Thursday (12/02/2010) Grade: Each problem is worth 10 points. Problem 8.1: Define two operators with given constants : Applying these two operators to a function ( ) , we may get ( ) and ( ) check if ( ) ( ) . What if we define the two operators as follows, check it again: ( ) ( ) ( ) ( ) ( ) ( ) Part 1 ( ) (( ) ( )) ( ( ) ( ) ( )) ( )( ( ) ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (( ) ( )) ( ( ) ( ) ( )) ( )( ( ) ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Part 2 ( ) (( ) ( )) ( ( ) ( ))

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2 ( )( ( ) ( )) ( ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (( ) ( )) ( ( ) ( )) ( )( ( ) ( )) ( ) ( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Problem 8.2: Solve the following system of equations with given initial conditions: { ( ) ( ) ( ) ( ) From (2) From (1) Characteristic Solution ( ) ( ) ( ) ( ) ( )

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