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

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

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
This is the end of the preview. Sign up to access the rest of the document.

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)...
View Full Document

This note was uploaded on 03/21/2010 for the course MATH 464 taught by Professor Staff during the Spring '08 term at Maryland.

Ask a homework question - tutors are online