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| − | + | [[Category:MA598RSummer2009pweigel]] | |
| + | [[Category:MA598]] | ||
| + | [[Category:math]] | ||
| + | [[Category:problem solving]] | ||
| + | [[Category:real analysis]] | ||
| + | |||
| + | =The Pirate's Booty= | ||
| + | Dead astern to [[MA_598R_pweigel_Summer_2009_Lecture_7|Lecture 7]] | ||
| + | |||
| + | * [[number one, ye scurvy dogs!]] | ||
| + | * [[number two, ye scallywags!]] | ||
| + | * [[number tree, argh!]] | ||
| + | * [[number 4, shiver me timbers!]] | ||
| + | * [[number five, me hearties!]] - Part (b) still be missing. | ||
| + | * [[number six, thar she blows!]] | ||
| + | * [[8 pieces o' silver]] | ||
| + | * [[number 9, me mateys]] | ||
| + | * [[ten barrels o' rum]] | ||
| + | * [[Number 11, Pirates Team]] - I was working on it at the same time you were, Nick. You just finished before I did so your version went up first. I figured that was what happened, but I wanted to make sure it got posted, regardless of who got it. Thanks, though :) | ||
| + | * [[number thirteen is walkin' the plank]] | ||
| + | * [[number fourteen (too lazy to come up with something else pirately to say)]] | ||
| + | |||
| + | |||
| + | |||
| + | ---- | ||
| + | '''Judgment Day''' | ||
| + | |||
| + | 1. You need absolute values everywhere. No points deducted, since it's clear you understand what you're doing, but it's sloppy to the point where you might offend a grader. | ||
| + | POINTS: 1/1 | ||
| + | |||
| + | 2. Good. | ||
| + | POINTS: 2/2 | ||
| + | |||
| + | 3. Good. | ||
| + | POINTS: 3/3 | ||
| + | |||
| + | 4. You have to remind the reader that <math>L^2(I) \subset L^1(I)</math>. I know what you're doing, but the grader might not. | ||
| + | POINTS: 4/4 | ||
| + | |||
| + | 5. Good. | ||
| + | POINTS: 5/5 | ||
| + | |||
| + | 6. You need continuity of <math>\hat{f}</math>! It seems implicit in the proof, especially since we already did that question, but this would be marked wrong on a qual. | ||
| + | POINTS: 5.9/6 | ||
| + | |||
| + | 7. Good. | ||
| + | POINTS: 6.9/7 | ||
| + | |||
| + | 11. The line involving the MVT is a mess. I would have no idea what you were talking about. Also, the <math>\displaystyle\lim_{h \rightarrow 0^+}</math> is superfluous (and wrong). A fix would be that there exists <math>\eta_h</math> such that <math>0< |\eta_h|< |h| </math>. You also need to cite Fubini/Tonelli when you interchange products. Full points awarded, however. | ||
| + | POINTS: 7.9/11 | ||
| + | |||
| + | 13. a) This one can't be saved. The definition of <math> ||\hat{f}||_{\infty}</math> is wrong, and you need that <math>\hat{f}</math> is continuous to conclude that <math>||\hat{f}||_{\infty} = \sup \{ |\hat{f}(x)| \} </math>. | ||
| + | |||
| + | b) As noted, the inverse fourier transform is only equal a.e. to f. Needs more work. | ||
| + | POINTS: 7.9/13 | ||
| + | |||
| + | 14. The change of variables is not correct. You need to replace <math>x</math> with <math>Ax</math>. Then <math>A^T A x = x</math> since <math>A</math> is orthogonal. | ||
| + | POINTS: 8.9/14 | ||
| + | |||
| + | TOTAL POINTS: 8.9 | ||
| + | |||
| + | ---- | ||
| + | [[MA_598R_pweigel_Summer_2009_Lecture_7|Back to Assignment 7]] | ||
| + | |||
| + | [[MA598R_%28WeigelSummer2009%29|Back to MA598R Summer 2009]] | ||
Latest revision as of 04:58, 11 June 2013
The Pirate's Booty
Dead astern to Lecture 7
- number one, ye scurvy dogs!
- number two, ye scallywags!
- number tree, argh!
- number 4, shiver me timbers!
- number five, me hearties! - Part (b) still be missing.
- number six, thar she blows!
- 8 pieces o' silver
- number 9, me mateys
- ten barrels o' rum
- Number 11, Pirates Team - I was working on it at the same time you were, Nick. You just finished before I did so your version went up first. I figured that was what happened, but I wanted to make sure it got posted, regardless of who got it. Thanks, though :)
- number thirteen is walkin' the plank
- number fourteen (too lazy to come up with something else pirately to say)
Judgment Day
1. You need absolute values everywhere. No points deducted, since it's clear you understand what you're doing, but it's sloppy to the point where you might offend a grader. POINTS: 1/1
2. Good. POINTS: 2/2
3. Good. POINTS: 3/3
4. You have to remind the reader that $ L^2(I) \subset L^1(I) $. I know what you're doing, but the grader might not. POINTS: 4/4
5. Good. POINTS: 5/5
6. You need continuity of $ \hat{f} $! It seems implicit in the proof, especially since we already did that question, but this would be marked wrong on a qual. POINTS: 5.9/6
7. Good. POINTS: 6.9/7
11. The line involving the MVT is a mess. I would have no idea what you were talking about. Also, the $ \displaystyle\lim_{h \rightarrow 0^+} $ is superfluous (and wrong). A fix would be that there exists $ \eta_h $ such that $ 0< |\eta_h|< |h| $. You also need to cite Fubini/Tonelli when you interchange products. Full points awarded, however. POINTS: 7.9/11
13. a) This one can't be saved. The definition of $ ||\hat{f}||_{\infty} $ is wrong, and you need that $ \hat{f} $ is continuous to conclude that $ ||\hat{f}||_{\infty} = \sup \{ |\hat{f}(x)| \} $.
b) As noted, the inverse fourier transform is only equal a.e. to f. Needs more work.
POINTS: 7.9/13
14. The change of variables is not correct. You need to replace $ x $ with $ Ax $. Then $ A^T A x = x $ since $ A $ is orthogonal. POINTS: 8.9/14
TOTAL POINTS: 8.9
