Math 4443/5443 Homework Assignments
Spring, 2010

Week 7: Mon. 3/1 - Fri. 3/5


Topics: Fundamental Theorem of Calculus, improper integrals, term by term integration of series
Homework:
4443 5443
      posted next week             posted next week      
Due date:
Announcements: There will be a quiz on Friday, March 26.

Week 8: Mon. 3/8 - Fri. 3/12


Topics: Open and closed sets of real numbers, interiors and closures, metric spaces and examples
Homework:
4443 5443
p. 149-52, #1, 2, 4, 10, 17, 18, 19 and the problems on this handout. p. 231-5, #13, 28; p. 149-52, #1, 2, 4, 10, 17, 18, 19 and problem #2 on this handout.
Due date: Wednesday, March 24, 2010
Announcements: The typo in #2d on the handout has been corrected. Please be sure you have the updated version.
This looks very long, but some of the Ch. 5 problems just require examples, not proofs.
There will be a quiz on Friday, March 26.
Exam 2 will be on Friday, April 9, 2010

Week 9: Mon. 3/22 - Fri. 3/26


Topics: Convergent and Cauchy sequences in metric spaces, functions on metric spaces
Homework:
4443 5443
p. 414-20, # 6, 15, 18, 19, 20, 29 p. 414-20, # 6, 9, 19, 20, 29
Due date: Wednesday, March 31, 2010
Announcements: There will be a quiz on Friday, March 26.
Exam 2 will be on Friday, April 9, 2010
#9 - just prove that rho is a metric on the set S of continuous functions and compare with the supremum metric on S. You do not need to worry about the density in X.

Week 10: Mon. 3/29 - Fri. 4/2


Topics: Limits and continuity of functions on metric spaces, compact sets.
Homework:
4443 5443
p. 149-52, #12, 13 and problems #2, 3, 5 on this handout. #6 on the handout can be done for extra credit. p. 149-52, #12 and problem #1-4 on this handout. #6 on the handout can be done for extra credit.
Due date: Wednesday, April 14, 2010
Announcements: Exam 2 will be on Friday, April 9, 2010

Week 11: Mon. 4/5 - Fri. 4/9


Topics: Limits and continuity of functions on metric spaces, compact sets.
Homework:
4443 5443
(same as above) p. 149-52, #12, 13 and problems #2, 3, 5 on this handout. #6 on the handout can be done for extra credit. (same as above) p. 149-52, #12 and problem #1-4 on this handout. #6 on the handout can be done for extra credit.
Due date: Wednesday, April 14, 2010
Announcements: Exam 2 will be on Friday, April 9, 2010. It will cover the Fundamental Theorem of Calculus, improper integrals, integration by parts, term-by-term integration of sequences and series, open and closed sets on the real line, metric space topics - open and closed sets, interior, closure, cluster points, examples - convergent and Cauchy sequences in metric spaces, completeness, limits of functions on a metric space, continuity, sequential characterization of limits and continuity, compact sets.
Just realized that I meant the book problems to be #12,13 on p. 416, not on p. 149. Well, I'll assign those next week!






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