HW9 - f that satisfy each of the following inhomogeneous...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Homework #9 Due: Tuesday, April 28, 2009 Note : Use of Matlab (or any other software) is not permitted. I. (Exercise 7.27) Find all generalized functions f that satisfy each of the following inhomogeneous equations. 1. (1pt) ) ( ) ( ) 1 ( 4 x x f x δ = ; 2. (1pt) ) ( ) ( ) 1 ( 4 x x f x = + ; Hint: Study exercises 7.23, 7.24. II. (Exercise 7.33, 7.36) Find the Fourier transform of each of the following generalized functions. In so doing, freely use the rules from the Fourier transform calculus together with the Fourier transforms we deduced in class. 3 . (1pt) ) ( ) ( 2 x e x f ix π = 4 . (1pt) ) cos( ) ( x x f = 5 . (1pt) ) ( ' ) ( x x x f = 6 . (1pt) ) ( ) ( 4 x sign e x f ix = 7. (1pt) 4 1 ) ( 2 = x x f III. (Exercise 7.27) Find all generalized functions
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: f that satisfy each of the following inhomogeneous equations. 8. (1pt) ) ( ) ( ) 1 ( 4 x x f D = ; 9. (1pt) ) ( ) ( ) 1 ( 4 x x f D = + ; Here D denotes the derivative operator. Thus ) ( ) ( 4 4 4 x dx f d x f D = . Hint: Fourier transform the equation, solve the algebraic equation thus obtained, and then Fourier invert the solution. IV. Find all generalized functions f that satisfy: 10 . (1pt) ) sin( ) ( ) 1 ( 2 x x f D = ; Hint: Use convolution with the Greens function, or Fourier transform the equation. Total : 10 pts (1 point each)...
View Full Document

Ask a homework question - tutors are online