Math 5616H, Spring '06

Last changed: April 10, 2006.

Old news: 4/10



Questions about Test 2, April 7:
(Q5) For Test 2, what from Chapter 9 will be covered?
(A5) The definition of derivative and the Chain Rule.
(Q4) For Test 2, what will "Fundamental Theorem of Calculus" mean?
(A4) It would have something to do with 6.20 and 6.21, depending on context.
(Q3) Do we need to know the problems from Assignment 9 for Test 2?
(A3) Yes. If you had trouble with one of them, ask!
(Q2) Which proof of integration-by-parts should we know for Test 2? May we use Rudin's,
which relies on the Fundamental Theorem of Calculus?
(A2) No, use the one from class.
(Q1) If material in the Riemann-Stieltjes notes on the Web was not covered in
class, must we study it for Test 2?
(A1) No, but it may help if you skim it to see how the material all fits together.

NEWS Apr 6: More questions about Test 2 (above).
Assignment 10 will be empty. There is an updated version of Section 6 on the
Web now. It includes some references to other sections and a restatement of a Theorem.

NEWS Apr 4a: More questions about Test 2 (above). A partial
solution of Special Problem 4 is posted.
NEWS Apr 2: Questions about Test 2 will remain at the top until Test 2 on Friday 4/7.
A few changes have been made in Section 5, and a new draft posted.
A typo in the Syllabus and the date for Test 2 have been corrected.
Some typos in Sections 1, 3 and 6 of the Riemann-Stieltjes notes have been corrected.

NEWS Apr 1: A (requested) solution for Special Problem 5 is posted. Its ideas
might be relevant for Monday's assignment.

NEWS Mar 29: A new version, a late draft, of Section 5 has been posted.

NEWS Mar 25: Reminder: Test 2 date, April 7.
Assignments are updated: Assignment 9 and Special Problem 6 (20 points).

NEWS Mar 24: All the Riemann-Stieltjes sections, except Section 5,
are now fair game for typo-finding!
Major News!: Test 2 has been moved to April 7!!

NEWS Mar 22: Assignment 8 is there now; my apologies.
Thanks to those of you who let me know it was missing!

NEWS Mar 21: Assignments are updated: Assignment 8. A newer
version, still a draft, of Section 3 is posted. The Lemma's proof is in it.

NEWS Mar 19: A new version, still a draft, of Section 3 is posted. It is still not
finished, lacking the proof of a lemma.

NEWS Mar 9: Assignments are updated: Special Problem 5 and Optional Special Problems
OP1 and OP2. Minor changes have been made in Section 6 of the Riemann-Stieltjes notes.

NEWS Mar 7: Very rough drafts of Sections 5 and 6 of the Riemann-Stieltjes
notes are now posted.

NEWS Mar 6: Assignments are updated: Assignment 7.

NEWS Mar 5: A very rough draft of Section three of the Riemann-Stieltjes
notes, on necessary conditions, is now posted. It addresses the double-discontinuity
barrier to existence. That is, in order for a Riemann-Stieltjes integral to exist
on a closed bounded interval, at every point of the interval at least one of f
and \alpha must be continuous. Section 3 is not finished!

NEWS Mar 4: Sections one two and four of the Riemann-Stieltjes notes,
in draft form, are now posted. Sections One and Four are essentially
what was in the existing notes (they will stay for now). Section Two is new.

NEWS Feb 27: Assignments are updated: Assignment 6, Special problem 4.

NEWS Feb 26: Our grader, Mr. Li, proposes to post some of your solutions
of homework problems on his Web site. I will ask about this in class Monday.
Please bring any homework papers you would be willing to allow him to use to class
on Monday as well.

NEWS Feb 17: Assignments are updated. Assignment 4 is empty, but
Assignment 5 is definitely harder. It would be good to get started now.

NEWS Feb 12: The first part of our alternate Chapter 6 is posted.
A link to our papergrader's Web page has been added, just above.

NEWS Feb 9: Our classroom has changed to VinH 20 (same as Fall's)

NEWS Feb 7: The material covered in yesterday's lecture is now posted.

NEWS Feb 5: Assignment 3 and Special Problems 1, 2 and 3 are posted.

NEWS Feb 4: A change in Assignment 2: Chapter 9, #9 should be changed.
Please change it from "c o n n e c t e d   open set E" to "open ball E of
positive radius" (still contained in R^n). If you wish, you can work with
"non-empty convex open set E" instead.

NEWS Jan 29: Assignment 2 has been added.

NEWS Jan 21a: A note on the discontinuities of an increasing function has
been added below. On Friday we covered 5.1 (frequently!) and 5.2, as well
as 9.10, 9.11 and some of 9.13. I plan to cover 9.10-9.21 while we're in Chapter
Five. Next time we'll discuss differentiation in yet another sense: the Complex
Sense, for we can still form a Difference Quotient of complex-valued functions
of a complex variable. We'll work with a useful and Very Important example, the
complex exponential function, defined by a power series.

NEWS Jan 19: Assignment and Syllabus are posted.


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