ANNOUNCEMENTS
MTH 434/534 — Winter 2015
- 3/20/15
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The final exams have been graded, and course grades have been uploaded
(but may not be visible until Monday).
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The average on the final was 51 out of 70, which defined the A/B cutoff.
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You can get your exam from me next term; if you are taking MTH 437, I will
return the exams in class.
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If there is sufficient interest, I will arrange an extra meeting to go over
the exam in detail.
- 3/18/15
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Here are the answers to the final exam questions:
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1. (a) 0 (b) ν∧ν≠0
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2.
(u×v)·w
= ∗(u∧v∧w)
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3.
dβ1≠0;
β2=d(x2y dz+df)
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4. 2 π2a4
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5.
(a) ∗1=ω,
∗dt=−r2sinθ
dθ∧dφ,
∗(r dθ)=r sinθ
dφ∧dt,
∗(r sinθ dφ)=
dt∧r dθ,
∗∗=−1.
(b) ∂2f/∂t2
−1/r2 ∂/∂θ
(sinθ ∂f/∂θ)
−(1/r2sin2θ)
∂2f/∂φ2
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6. K=−1/a2
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EC: 1/2 π2a4
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Worked solutions can be seen in my office, but probably not until next term.
- 3/14/15
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Today is both Einstein's birthday and Pi Day.
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Details of tomorrow's review session are in a previous post below that
was inadvertently hidden until today.
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A formula sheet will be available on the final. You can find a
copy here.
- 3/13/15
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Strange but true: The 13th of the month is more likely to be a Friday than
any other day of the week!
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Give up? Further information is available here.
- 3/12/15
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There will be an exam review session on Sunday, 3/15, at 4 PM, in Weniger 149.
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I have booked the room until 7 PM, and will stay as long as there are
questions.
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I also expect to be in my office most of Monday, 3/16.
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Feel free to drop in, or send me an email message to arrange an appointment.
- 3/11/15
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There will be no class on Friday, 3/13/15.
- 3/10/15
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The final will be Tuesday 3/17/15 from 2–3:50 PM in Weniger 149 (our
regular classroom).
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- The exam is closed book.
- The exam will cover everything discussed in class through Wednesday
3/11/15.
- The final will be slightly less than twice as long as the midterm, and
will cover material from the entire course.
- Important new topics are the structure equations and curvature.
- Important old topics are exterior product (∧), Hodge dual (∗),
and exterior differentiation (d).
- Other topics discussed in class this past week should be regarded as
supplementary material which is good to know but not required.
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There will be a review session at one of the following times: Sunday 3/15 at 2
PM, Sunday 3/15 at 7 PM, Monday 3/16 at 2 PM.
Please be prepared to help choose a time during class on Wednesday.
- 3/9/15
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As was pointed out to me after class today, I misstated the necessary
condition for the converse of the Poincaré Lemma to hold. Here's a
correct version:
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Let D be a contractible region of Rn. Then every closed p-form on
D is also exact.
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A contractible region is indeed one with "no holes", but such a region can
still be simply connected, which instead asks whether curves can be
contracted. In particular, the sphere is simply connected, but not
contractible.
- 3/8/15
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Two mathematicians are talking on the telephone. Both are in the continental
United States. One is in a West Coast state, the other is in an East Coast
state. They suddenly realize that the correct local time in both locations is
the same! How is this possible?
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Give up? Some hints can be found here.
- 2/25/15
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The homework assignment due this Friday will be accepted
without penalty until Monday 3/2.
- 2/24/15
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Due to multiple job searches, my office hours are subject to change over the
next few weeks.
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Please don't hesitate to simply try to find me in my office, or to email me
for an appointment at another time.
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Friday 2/27:
My afternoon office hour is canceled.
I expect to be in my office from 11–11:45 AM, and am available after
class.
UPDATE:
There is a good chance I will also be in my office from 2–2:45 PM.
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Monday 3/2:
My afternoon office hour is postponed.
I currently expect to be in my office from 11–11:45 AM, as well as
from 2:15–2:45 PM.
- 2/23/15
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There is a significant typo in the text:
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In both (17.4) and (17.5) on page 204, there should be no factors of r on the
RHS
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There is also a minor typo in the caption of Figure 17.1 on page 203:
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θ-hat should be φ-hat.
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Both errors have been corrected in the
wiki version of the text
- 2/17/15
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Here are the answers to the midterm questions:
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1.
(a) τ∧τ
= 2 dx∧dy∧dz∧dt
∈∧4;
dτ = 0 ∈∧3
(b) σ = x dy + z dt
(Other answers are possible.)
(c) FALSE
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2.
(a) ∗(dh∧∗dh)
+ h ∗d∗dh
(b) ∇·(h∇h)
= ∇h·∇h
+ h△h
(c) Yes (Other answers are possible.)
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3.
(a) du∧dv + dw∧ds
(b) du∧dv − dw∧ds
(Other answers are possible.)
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4.
(a) h2dq∧dφ
(b) (∂2f/∂q2
+∂2f/∂φ2)/h2
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EC: 2 π2r3
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Worked solutions can be seen in my office, and will be discussed in class
tomorrow.
- 2/14/15
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The answer (but not the solution) to HW 5 in
parabolic cylindrical coordinates can be found here.
- 2/13/15
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Strange but true: The 13th of the month is more likely to be a Friday than
any other day of the week!
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Give up? Further information is available here.
- 2/10/15
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A formula sheet will be available on the midterm. You can find a
copy here.
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2/2/15
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I have posted next week's homework assignment early, so
that you can get a head start on it.
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If this assignment is turned in by the posted due date of W 2/11, it will be
returned to you by F 2/13.
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Assignments turned in by F 2/13, will count as on time, but are unlikely
to be returned to you before the midterm.
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Don't forget to do this week's homework assignment first!
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2/1/15
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The midterm is scheduled for Monday, 2/16, in class.
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- The exam is closed book.
- The exam will cover everything discussed in class through Friday 2/13/15.
- Important topics are exterior product (∧), Hodge dual (∗), and
exterior differentiation (d).
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1/27/15
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I may be a few minutes late for my office hour tomorrow (Wed) morning...
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1/26/15
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The class has been moved permanently to Weniger 149, effective today.
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1/25/15
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There is a minor typo in the homework:
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In problem 1(d), both instances of z should be w.
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The posted homework assignment has been corrected.
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1/23/15
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Today's class (Friday 1/23) will meet in Weniger 149.
- 1/20/15
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In this week's homework, you may assume that H is a constant
1-form, that is, that each of Hx,
Hy, Hz are constant.
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By all means consider the case where these components are functions for
extra credit.
- 1/19/15
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I will likely be in my office tomorrow, Tuesday 1/20/15, from roughly
10–11:45 AM, 1–1:30 PM, and 3:30–5 PM.
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I will be in meetings from 1:30–3:30; if they run over, I may be a few
minutes late.
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(If you can't find me, email should reach me quickly.)
- 1/16/15
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I have posted one possible solution to the first
homework assignment.
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If you didn't get the score you were hoping for on this assignment, don't panic!
A single assignment is not enough to ruin your chances for a good course
grade — I plan to drop the lowest homework score or two anyway.
I encourage you to stop by my office to touch base with me about how things
are going.
- 1/14/15
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You are strongly encouraged to work on course material
together with others in the class, that is, to organize or join a study
group.
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The ground rules explicitly permit working on homework
problems together, so long as you write up the solution in your own words, and
you acknowledge your sources.
If you do homework with others, you should say so explicitly, and include a
list of names of those you worked with.
- 1/10/15
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In addition to my posted office hours, you are welcome to drop in to my office
(almost) any time I am there.
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Good times to find me are before and after class (except on Mondays when there
is a math or physics colloquium). In addition, I am often in my office on MW
(and some F) mornings. However, I am usually difficult to find on TR, with T
afternoon being the most likely — make an appointment!
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Most students on the waitlist should now be able to register.
Contact me ASAP if you are unable to do so.
- 1/9/15
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Here is the list of basic linear algebra topics we came up with in today's
class.
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- vector space
- linear (in)dependence
- basis
- change of basis
- span
- linear transformation
- eigenvalues
- eigenvectors
- determinants
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You should review these topics if you are rusty!
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You can "review" vector calculus using the language of dr
and dA via our
online
vector calculus text.
- 1/6/15
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There will be no class on Monday, 1/12/15.
- 1/5/15
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Textbook availability:
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The book is currently being reprinted. It should be available in a
week or two, but there are no guarantees.
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If you can find an online seller with availability, you may want to grab a
copy there.
The bookstore has a
price comparison tool,
which they claim shows availability.
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I bought a few copies myself, which I am willing to sell for the bookstore price
($48).
First come, first served; send me an email if interested.
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Until you get a copy, you can use the
ebook
from the library.
- 1/4/15
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The text
can be read online as an
ebook
through the OSU library.
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There is also a freely accessible
wiki
version available, which is however not quite the same as the
published version.
- 1/3/15
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Both the instructions and the due date for the
first homework assignment
have been changed slightly.
- 1/2/15
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The course remains full. If you are on the waitlist, please make sure to come
to class.
- 11/21/14
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Both MTH 434 and MTH 534 are officially full.
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It is likely that 5–10 additional spaces will be made available.
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To maximize your chances of getting in, make sure to get on the waitlist
and come to class.
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Waitlisting is not available until
Phase II.