Math 2300 Elementary Linear Algebra: Team Project N. Mackey ...

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Feb 12, 2013 ... Elementary Linear Algebra: Team Project. N. Mackey. Submit solutions to problems worth a total of 50 points. This assignment is worth.
Math 2300

Elementary Linear Algebra: Team Project

N. Mackey

Submit solutions to problems worth a total of 50 points. This assignment is worth 7% of your grade in the course. Work in teams of 2 students per team. If you cannot decide on a teammate, then I will assign you to a team. This is a writing assignment. This means that you must explain your solutions, using complete sentences, correct grammar and correct mathematical notation. No credit for answers alone. No credit for untidy, illegible work. When you are initially working through a problem, you might produce some scratchwork. Scratchwork has to be turned into a properly written solution for submission. Scratchwork is unacceptable as your final submission, and it will earn NO credit. Model solutions to mimic are the solved examples posted on the class website at http://homepages.wmich.edu/ mackey/Teaching/230/index.html Requirements for good team work: 1. It is NECESSARY to work on your own first. Each team member must work independently on the chosen problems in order to have a meaningful contribution. 2. Critique each other’s work in a constructive way. 3. Writing must distributed approximately evenly among all members. 4. Your final submission must contain an honest, signed, self evaluation by each team member of their contribution to the project. Use this as a cover page for your final submitted work. Team Members: Checklist for submitted work: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

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Has the statement of the problem been included? Does each solution begin on a new page? Is your submitted work neatly written? Is it organized? Is it legible? Is the logic explicit? Have you used correct mathematical notation? Have complete sentences been incorporated? Are the sentences grammatically correct? Have you used a dictionary if you were unsure of how to spell a word? Has all crossed-out work been removed/erased/replaced? Have you communicated your understanding clearly? Have you each submitted an honest, signed, self-evaluation?

Deadlines: You must form your team and report it to me by email by March 15. Your team must discuss your progress on this project with me in person by March 29. Final project is due April 12.

Instructions: In addition to the previous cover page, submit this list of problems with your chosen problems clearly circled/highlighted. The values of the problems you select must total 50 points. Team Members:

1. 2. 3. 4. 5. 6.

(5 pts) p.25, Problem 15 OR p.26, Problem 20 OR p.26, Problem 22. (5 pts) p.57, Problem 18 OR p.57, Problem 20. (5 pts) p.67, Problem 14 OR p.67, Problem 19. (5 pts) p.77, Problem 17 OR p.77, Problem 18. (10 pts) p.126, Problem 22 AND p.144, Problem 16. (5 pts) p.126, Problem 23. In each case, if true, give a proof, and if false, give a counterexample. 7. (5 pts) We saw in class that C 1 [−1, 1] is a proper subset of C[−1, 1]. We did this by exhibiting a funcion that is continuous on [−1, 1] but not differentiable, namely the function f (x) = |x|. This problem extends this result, showing that C n+1 [−1, 1] is a proper subset of C n [−1, 1], for every positive integer n. (a) Consider the function f1 defined by { x2 f1 (x) = −x2

if x ≥ 0, if x < 0.

Prove that f1 ∈ C 1 [−1, 1] but f1 ∈ / C 2 [−1, 1]. Include a neat, labeled, and carefully drawn graph of f1 . (b) Extend this idea to construct analogous functions fn for each positive integer n, so that fn ∈ C n [−1, 1], but fn ∈ / C n+1 [−1, 1]. Justify your answer. Include neat, labeled, and carefully drawn graphs of f2 and f3 on [−1, 1]. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

(5 pts) p.138, Problem 18. (5 pts) p.144, Problem 17. (5 pts) p.144, Problem 18. (5 pts) p.175, Problem 13. (5 pts) p.175, Problem 15. (10 pts) p.175, Problems 21 AND 25. (5 pts) p.195, Problem 15. (5 pts) p.213, Problem 18. (5 pts) p.213, Problem 19. More to come....

Last Updated: Tuesday 12th February, 2013,

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