Due date for 5,6,7,9,11: Mon. 4/20/09.
- Problems D4 and D5 from Homework 4. Add this part (f) to D5:
(f) Did any of parts (b) through (d) of this problem involve interchanging the order of a limit as n goes to infinity and an integral? Would such an interchange even have been possible? Why or why not?
Due date: Fri. 4/17/09. D5, from part (b) on, is very straightforward; you should all be able to do it and arrive at a fun cocktail-party fact. Note that in D5, you are allowed to use the results of D4, whether or not you succeeded in doing D4. Also, if you don't succeed in doing part (a) of D5, you are allowed to assume it to do the rest of the problem. Hint for part (a): this is one of those rare instances in which even a real mathematician might use L'Hopital's Rule.
- Miscellaneous non-book problems. This list will be updated as I add more problems; keep checking back.
Due date for F1: Mon. 4/20/09.
Due date for F2: Wed. 4/22/09.- Here is a handout: Matrices, Power Series, and Functions of Matrices. You should read this handout and (eventually) do as many of the problems as you want to hand in for extra credit (I have not decided point-values yet). Based on where we finished lecture on Wed. 4/17/09, you should now have enough information to do all the problems, except that I forgot to mention this bit of terminology: when we say a function is differentiable without specifying at what point, we mean "differentiable at every point of its domain". None of the problems are hard (compared to problems I've assigned you before), but some are easier than others.
Of course, you still need to read what's interspersed between the problems.
I fixed some minor typos on p. 4 on 4/17/09. If you printed out an earlier version and it looks like some words were left out of a sentence, check the updated version.
Due date for 1,2,4,8,10: Wed. 4/22/09.