Homework-8-s11-solution

Homework-8-s11-solution - AMS 361: Applied Calculus IV (DE...

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1 Homework 8 Assignment Date: Wednesday (03/23/2011) Collection Date: Wednesday (05/04/2011) Grade: Each problem is worth 10 points Problem 8.1: Define two operators: ! ! = ! ! + ! + 1 ! ! = ! ! + 2 ! Applying these two operators to a function ! ( ! ) , we may get ! ! ! ! ! ( ! ) and ! ! ! ! ! ( ! ) check if ! ! ! ! ! ! = ! ! ! ! ! ( ! ) . What if we define two operators as follows, check it again: ! ! ! ! !" ! + !" ( ! ) ! ! ! ! !"# ! + ! ( ! ) Solution: First, let’s check ! ! ! ! ! ( ! ) : ! ! ! ! ! ! = ! ! !"# + ! = ! !"# + ! + !"# + !" = 2 !" + ! ! ! ! + !"# + !" Then, let’s check ! ! ! ! ! ( ! ) : ! ! ! ! ! ! = ! ! !" + !" = !" !" + ! + !" + !" = 2 !" + ! ! ! ! + ! ! !" + !" Obviously, ! ! ! ! ! ( ! ) ! ! ! ! ! ( ! ) . Problem 8.2: Solve the following system of equations with given initial conditions: ! ! = ! 2 ! ! ! = ! ! ! 0 = 2
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This note was uploaded on 05/09/2011 for the course AMS 361 taught by Professor Staff during the Spring '08 term at SUNY Stony Brook.

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Homework-8-s11-solution - AMS 361: Applied Calculus IV (DE...

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