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Unformatted text preview: AMS 361: Applied Calculus IV by Prof Y. Deng
Homework 8
Assignment Date: Collection Date:
Grade: Tuesday (11/09/2010) Thursday (12/02/2010)
Each problem is worth 10 points.
: Problem 8.1: Define two operators with given constants ( ) and () Applying these two operators to a function ( ), we may get () ( ). What if we define the two operators as follows, check it check if again: () () () () () ()
Part 1 () ( ( () ( ) () ( () ( ( () ( ) () ( () Part 2 () )( () ) () (( () () )( () ) () (( () ) ( )) ( )) () ( ) ( )) ( )) () ( () ( )) ) () () ( )) ) () () () ( (( () ) ( )) ( )) 1 ( ( () () () ( )( () () ) (( ( )) () () () () () ( ( () ( () () ( () ) ( )) ( )) () )( () ( )) ) ( )) () () () () () Problem 8.2: Solve the following system of equations with given initial conditions: () () () () {
From (2) From (1) Characteristic Solution () () () () () () () 2 Since ( () () () () () () () ) () ( ) () Problem 8.3: Solve the following system of equations by (1) substitution method and (2) operation method: () { ()
Substitution Method From (2) Using (1) Characteristic Solution √ √ ( ( √ ) ( ( √ ) ) ( √ ( √ )) ) ( √ ) √ Since (( √ ) ( √ ) ( √ ) ( √ ) 3 () (( √ ) () ( ( ( √ ) ) ( √ √ ) ( )) ( √ ) √ Operator Method   (( ( Characteristic Solution  )( ) ) ( ) )( )  √ √ () √ ( ( √ ) √ ( √ )) √ () (( ) ( ) ( √ ) ( )) Problem 8.4: Find the general solution of the following. () { () ()
From (3) From (2) From (1) 4 ( ( ) ) Characteristic Solution Particular Solution ( ) ( ) () ( () () ( ) ) Problem 8.5: Use operational determinant method to solve the following system of equations: ( ) ( ) () { ( ) ()
    5    ( )    () () 6 ...
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This note was uploaded on 01/31/2011 for the course AMS 361 taught by Professor Staff during the Fall '08 term at SUNY Stony Brook.
 Fall '08
 Staff

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