Questions, comments and answers.
22 November 2006.
Text book Calculus: A Complete Course, R. A. Adams, 5th Edition, Addison Wesley Longman. I just thought I'd mention this book for the class to use, It contains all of the course content studied up to this point, vector fields, line integrals, surface integrals, etc... are covered.
Reply Great, thanks.
23 November 2006.
Conservative fields Curl F = 0 implies F is conservative. Is the converse true iff the domain is simply connected?
Reply It is true that conservative implies curl F=0 on a simply connected domain, we will prove that next week using the Stokes theorem.
11 December 2006.
Schols Im planning on taking the scol exam, and am wondering what books and the like i should be reading. Could you e-mail me back a few titles please?
Reply Although the schol questions may be more challenging the course is the
same, the schol exam will be based on that part of the course which
has been covered at that point.
7 January 2007.
small typo Hello small typo on page 6 of soln123.ps at the bottom it says 1/2pi instead of pi/2
Reply Thanks, fixed it!
11 January 2007.
Vector Identities I'm just wondering do we need to know the statements of the nine vector identities we did, or will we be given those or similar identities on exams and asked to prove them?
Reply I would be most likely to ask you to prove them from the statement,
however, the ones that are used in other important constructions and
proofs appearing in the notes, you would be expected to know in that
context. Also I would expect you to know:
div grad phi=laplacian phi
curl grad phi =0
div curl F=0.
31 January 2007.
Schol solutions Hey, was just wondering if you could post solutions to a few of the past schols exams or if I could collect them from you or something?! Thanks a million.
Reply Good point, I will do up solutions for last years schols. I am working on catching up 231 stuff at the moment, note the addition of 231.II.1 to the notes page, so hopefully it will get done soon!
8 February 2007.
Tutorial Solutions Hi, I have heard
along the grape-vine that some members of the 231 class have been
using last year's website to obtain answers to the problem sets. I
don't know if this has been happening for long, but I think that it is
very unfair on those of us that are actually trying the problems
ourselves, and not just copying old solutions.
Reply That's
a pity, the marginal benefit in marks from copying the previous years
solutions will not make up for the big loss in the usefulness of the
tutorials. One problem with continually assessed graded work is that
it is hard to control this sort of thing; that is why, unfortunately,
it can only contribute a small fraction of the final exam. Again,
copying in this way is likely to hinder rather than benefit the copier
and is not really worth worrying about as an issue of
fairness. However, it is something I need to worry about from a
teaching point of view; in future I will make sure the questions on
the marked problem sheets are at least partly new.
11 March 2007.
Schol 2006 solutions. Hello, sorry about this but the link for the solution to Q 5/6 for last year's schol paper doesn't seem to be working. There's no huge rush on it bit it would be handy to have it within the next week or so. Thanks!
Reply This should be working now. Thanks.
28 March 2007.
Last year's Schol paper.
Hi, I realise that it is probably too late to get a reply before the exam, but for future knowledge, I was wondering about Q5 on last year's Schol paper. In your solutions you appear to use a period of two pi, however surely the absolute value of cos has period pi, since |cos(0)|=|-1|=|1|=|cos(pi)|. Thanks.
Reply Yes good point, it is a lot easier if you use that. What I did works too because it does repeat every 2 pi, but it is easier and clearer
using the periodicity. I will change it. I thought as I was
doing it that it seemed more fiddly than when I did it last year! Thanks a mill
28 March 2007. typo
hello typo on notes Part I.6 on first page F=F3k not F3i
Reply Thanks!
30 March 2007. schol
Hi,
I was just wondering about question 4 in the exam. Is the formula
quoted,
curl curl F = laplacian F - grad div F
correct?
During the exam I calculated the RHS as grad div F - laplacian F.
Thanks,
Reply You are correct; I will mark accordingly. I am sorry about the error.
17 April 2007.
Homework 18 Q4
Hi Conor, Should the -2ny be +2ny due to definition of Hn(x) as given in the notes? In the notes we had that Hn(x) was the solution when alpha was equal to n. Thanks.
Reply Yes, thanks, I will change it now.