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This page is for exercise lists and various other announcments. I will probably update it every week or two, and will include remarks on Exam topics as those draw near. The dates and content are subject to change, but such changes will be posted here in advance. I suggest checking this page at least once a week, and more often near the Exam dates. I don't plan to collect homework (HW) for grading, but will assign selected problems for you to practice with [see below], which we can discuss on the dates given below. If you want to hand in your HW, I will look it over, try to answer any issues / questions I see, and return it promptly. I may give a little extra credit at the end, if you do this consistently and well.

Most of the exercises will come from the Walter text, and I will use his numbering system. For example, exercise (a) at the top of page 24 is in Chapter.1, Section 1, subsection XIII, so I would call it "1.1.XIII.a". If the Chapter number is understood, I may omit that and write "1.XIII.a" instead. I will probably also write up some additional exercises, as needed, and post them on separate web pages.

I have also posted an outline of topics , which includes a list of vocabulary (not complete,of course) that you should have picked up from previous courses. It might be a good idea to review that as needed during the first week(s) of the term. There is a second list that you might have picked up; I will probably have to review these in class, but if they are new to you, some proactive work on them is advised. For example, I cover Cauchy sequences and completeness in my MAA 3200 course, but am not sure all profs do so.

HW 1 for Thursday Jan 19 -- from Ch 1

Note that there is an Answer Key in the back, not all problems are labelled correctly. Example; Problem 3.IXa is answered, but mis-labelled as 3.VIIIa. You may omit the second part of that one ("Discuss..."), or not take it too seriously. It seems quite difficult to do exactly.

* review the vocab lists mentioned above
* review your MAC 2302 text (undergrad DEs), about special types of ODEs (separable, exact, homogeneous, etc)
* Do 1.XII.a, 1.XIIIadgj, 2.Vab, 2.VI, 3.VIIIa, 3.IXabd, and the
exercise from class; check that "Im[dz/z]=0" seems exact [dg/dy = dh/dx] but it is not, if D is not simply connected.
* remember to recheck this page for additions or changes.
* read most of Ch 1.1 thru 1.3. You may omit the "Supplement" and the theorem on page 17.

Christian asked a nice question in class [1/19], about the number of line elements per region in the plane - here is a fairly detailed answer.
Please read pgs 53-58 before Tuesday 1/24, and let me know ASAP if you need any help with that. Otherwise, I will begin Tuesday with contractive mappings (see page 59) and fixed points in Banach spaces.

HW 2 for Thursday Feb 2 -- from Ch 1-2.

* Ch1 4.VIIIab
* Ch 2.6 VIII, IX, XV
* Prove carefully that the sequence x_n in the Fixed Pt thm is Cauchy.
* Read thru pg 80.

Exam 1 is Thursday, Feb 9, mainly Chs 1-2 through p75. See this review sheet for a list of proofs to know, etc. Last Minute FAQs: 1) Know the proof of AA on pg75 (I think this is clear from the revised review sheet, but I was asked about this). 2) Exercise 3.VIIIa refers to "Theorem VI", but it is unclear which Theorem this is. In my opinion, you are supposed to go through the discussion on pages 43-44 and probably refer to Thm 3.VII (not sure).
Approx Feb 12 - The key and scale have now been posted on the exam page.

HW 3 for Thursday Feb 16, or asap, from Ch 2

p79 VIII both
p81, XI [and read XII carefully]
p83 XV
p88 IVab
Read though page 89. Omit p83 XVI. Let me know if you have any problems, with the complex ODEs, for example.

HW 4 for Thursday Mar 1, from Ch 2-3

p90 from lecture, that p(a)>0. See the link below for more details.
p94-95, VII/rk (b) , the part about "full of solutions".
p98 XIIab [it is OK to use the Key for this, and to omit "Lohner"]
See HW from lectures. [updated on 3/3/12 to include HW from recent lectures]
p120abc
p131ab

Read through approx page 135. We will probably omit the last part of Ch2, from pg 95 to pg 104, but I think you can do the HW on page 98 anyway. Omit Supp I-II pgs 111-125. Except - do read XV-XVII, pgs 117-121. I expect we will cover most of pgs 125-135, tba in class approx Mar 1.
Summary; read pgs 89-95, 104-111, 117-121, 125-135.

Spring Break Mar 12-17

It seems we will not have time to cover everything this term. I intend to cover most of Chs 4 and 7, and then 5 or 6, as time permits. If you have any concerns about this, please let me know ASAP.

Exam 2 is Tuesday, Mar 20 - on Chs 2-3, including the Mar 6 lecture. Roughly, it covers pages 75 to 157, omitting pages mentioned above. Know HW 3-4, of course, and perhaps the first problem in HW5 below (because it relates to the March 6 lecture).
Main Proofs: See p81 and 90 (both easy!), p106-107, p108 (part c only, either the lecture or textbook proof is OK), p118, and the Estimation thm on page 144 (not including the Dini aspects). I might also ask you to discuss the catenary problem, though it is not really a proof.

HW 5 for Thursday Mar 22, Ch 4

Fill in the details of the proof of equation 14.5, page 161.
VIII on p163, IX on page 164. There were some questions about these two. See my answer key to these, if needed.
VIabc on page 169

HW 6 for Thursday Mar 29, Ch 4.

Read through the top of page 195, omitting the Supp on page 173 (maybe more tba). Do:
IV, p172. Responding to a question, here is a partial answer and a sketch of the solution.
Prove the claim on p183, approx line 11, that m' cannot exceed m. Also, be sure to go over Example IX, p 183.
Prove the claim on p185, approx line 12, "...there is a vector d so that ..."
XII, p189, abc
XIII, p189 ac only
VII, p194, do "a" only

Abdellah suggests another online textbook , which may help with both ODEs and Linear Algebra background topics.
We are skipping from page 195 to Ch. 7 for now, returning to the omitted topics if time permits.

HW 7 -- Ch 7

X and XI on page 317
More practice problems

Any late work, doctor's notes, any misc business should be settled by Tues April 17.

Final Exam, Tuesday, April 24, 5pm to 7pm. Covers all topics, with emphasis on Chs 4 and 7. Proofs to know [shortened slightly on 4/21] - 15.III pg 166, 29.III pg 307, 29.VII pg 311, 30.IIab pg 319, 30.V pg 323. I probably wouldn't ask for all of the 29.VII proof, but might ask for some piece of it. I am more interested in the second paragraph of the 29.III proof than the first. Be able to explain formula 17(13) as done on page 181 or as done on page 193. Review 17.X pgs 184-188 (be able to work out most of the cases). Be able to work out long examples like those in early Ch.4 (pg 178, for example), though I may do some of the work for you to save on exam time and minimize silly calculation errors. Read Ch 7 through Theorem 30.VIII pg 325 (I will not ask for the proof since we did not get to it on 4/19).

Notice the new link "More practice problems" under HW7, posted approx 4/16. Also TWO new links under HW6 for pg 172, posted 4/18 and 4/21.

I am assuming that near the end, you will put more effort into Chs 4 and 7 than Chs 1-3. But those older topics might be up to a third of the final, so review those as needed. I may post more tips here approx 4/20, especially if I cannot answer all your questions in class on 4/19. I will not have regular office hours after 4/19, but you can always email me, and I may have some office time on 4/24 just before the exam.