527ass8 - hint given: with this it can be done by...

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

View Full Document Right Arrow Icon
642:527 ASSIGNMENT 8 FALL 2009 Turn in starred problems Tuesday 11/03/2009. Section 9.9: 4 (a), (e)* Section 9.10: 2 (a), (c)*; 3 Section 17.2: 5 (a), (e), (g); 12 (a), (e), (j)*, (s) Section 17.3: 1, 4 (a), (c)*, (l)* 8.A* Exercise 1 from the notes on Expansions in Orthogonal Bases, available on the web page. Comments: (a) For the problems in Section 19.10: the best approximation to a given vector within the “span” of some vectors { e 1 , e 2 , . . . } means the best approximation as a linear combination of those vectors. (b) 17.2 12(j) is a bit tricky—think carefully. On the other hand, 17.3 4(l) is easy, if you use the
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: hint given: with this it can be done by inspection. The two problems are related. (c) The extra exercise 8.A involves the evaluation of many integrals; these are simple (just poly-nomials) but it is still a nuisance. You are welcome to use Maple, Mathematica, or some other program to do these. If you do so, write the integral out out explicitly before giving the answer. For example, for part (a) you might write a f, g A = i 2 f ( x ) g ( x ) dx = i 2 (1 x ) dx = 0; a g, g A = i 2 g ( x ) 2 dx = i 2 (1 x ) 2 dx = 2 3 , so b g b = r a g, g A = R 2 3 ....
View Full Document

This note was uploaded on 12/15/2009 for the course MATH 527 taught by Professor Staff during the Fall '08 term at Rutgers.

Ask a homework question - tutors are online