HW7 - 27 − = = x x x x x x x f 8(1pt 2 1 x x p x f =...

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Homework #7 Due: Tuesday, April 14, 2009 Note : Use of Matlab (or any other software) is not permitted. (Exercises 7.8, 7.11) Find and simplify the functional f{ Φ } , Φ∈ S , that is used to represent the generalized function f when: 1. (1pt) ⎣⎦ x x f = ) ( 2. (1pt) ) 2 ( ' ) ( x x f δ = 3. (1pt) | | log ) ( x x f = 4. (1pt) ) ( ' ) ( x x f Π = 5. (1pt) ) 5 ( ' ' ) ( = x x f 6. (1pt) () ⎣⎦ ' 2 / 1 ) ( = x x f 7. (1pt) () () () 2 2 2 2 1 3 1 2 4 3 4 2 4 5
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Unformatted text preview: 27 : ) ( + + + − + + + = + + = x x x x x x x f 8. (1pt) ) 2 ( ' ) ( ) ( 1 x x p x f = , where ) ( 1 x p is defined in Section 7.2 9. (1pt) ( ) ) ( ' ) ( 1 x p x f − ∗ = , where ) ( 1 x p − is defined in Section 7.2 10. (1pt) ) ( ' ' ) ( ^ s s f = Total : 10 pts (1 point each)...
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