HW6 - symbolic integrals, not Riemann or Lebesgue...

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Homework #6 Due: Tuesday, April 7, 2009 Note : Use of Matlab (or any other software) is not permitted. 1. (Exercise 7.4) Use the mesa function from Figure 7.5 of the textbook to construct two Schwartz functions Φ (one for case (a) below, and another one for case (b) below) with the following properties. a. (1pt) Let - <a<b<c<d< and let p be a polynomial. Construct Φ∈ S such that (x)=0 f o r x a or x d; (x) lies between p(x) and 0 (that is | (x)| |p(x)| ) for a x b or c x d ; and (x)=p(x) f o r b x c . b. (1pt) Let a 0 ,a 1 ,…,a n be constants and let ε >0. Construct Φ∈ S such that (0)=a 0 , ’(0)=a 1 , … , (n) (0)=a n ; and (x)=0 for |x| ≥ε . 2. (Exercise 7.7) Find the value of each of the following “integrals” (these are
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Unformatted text preview: symbolic integrals, not Riemann or Lebesgue integrals). a. (1pt) dx e x x 2 ) 2 ( b. (1pt) dx e x x 2 ) ( ' c. (1pt) dx e x x 2 ) 2 ( ' d. (1pt) dx e x x 2 ) 1 ( ' e. (1pt) dx e x x 2 ) ( ' ' f. (1pt) [ ] dx e x x x 2 ) ( ) cos( g. (1pt) [ ] dx e x x x 2 ) ( ' ) sin( h. (1pt) ( ) dx e x x 2 ) ( ' ' Total : 10 pts (1 point each)...
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This note was uploaded on 03/21/2010 for the course MATH 464 taught by Professor Staff during the Spring '08 term at Maryland.

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