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#226 Re: Help Me ! » Complex Transformations » 2011-07-02 04:16:39
Hi anonimnystefy,
Yes, you're quite right - thanks, I hadn't noticed that mistake. Unfortunately, the rest is still wrong 
#227 Help Me ! » Complex Transformations » 2011-07-02 03:08:34
- Au101
- Replies: 10
Hi guys,
I'm completely confused by this question I have on complex transformations.
In order to do part a) - which I was able to do fine - I found that:
For part b) - then - I used this fact to say that:
But this does not give me the right answer. Upon looking-up how it was done, I was told that:
And I can't for the life of me see why this should be the case
Can anyone help? Thanks 
#228 Re: Help Me ! » Roots of a Complex Number » 2011-06-26 05:18:01
Perfect - thank you everyone
#229 Re: Help Me ! » Roots of a Complex Number » 2011-06-26 04:36:56
Hello, there, anonimnystefy - I agree with you on part a. but it's nice to have my answered confirmed. As for your answer to part (c) - that makes an awful lot of sense, I think that you're absolutely right. I can definitely justify that answer, but I'm not sure how I would go about deriving it. Could you advise me on how to set-out an answer?
Edited to add: Hi gAr - sorry, I was replying when you replied. Thanks very much . I don't suppose that you could help with my second question as well?
Thanks a lot:)
#230 Help Me ! » Roots of a Complex Number » 2011-06-26 04:11:04
- Au101
- Replies: 7
Hi guys,
I have a bit of a problem with the following question:
My answers to part a. are as follows:
Which I believe to be correct. The answer book actually gives the answer as:
However, I do not think that this is right. Even if this is right, it doesn't help me with part c. The answer which is given is that the centre is (0,0) and the radius 1. 1, of course, is the magnitude of both:
Which makes sense, however, how can these points form a circle when the third root is at -2. Surely the radius must be 2 - I simply don't understand
Thanks
#231 Re: Help Me ! » Definite integration (by parts) » 2011-06-20 12:40:00
Hi guys - Yeah C4 was my last exam for this year, so I'm hoping to use my holiday to get to grips with some more interesting stuff . Thanks bobbym - I certainly enjoyed it, I don't know if I did well or not, but I was happy with what I managed so I suppose I just have to wait and see
#232 Re: Help Me ! » Definite integration (by parts) » 2011-06-20 04:45:51
Hey everyone - the examination this morning was pretty difficult. In fact I made a big mistake on an IBP question and was only able to fix it right at the very end - I knew I'd done something wrong, when I got a negative area . It was fairly enjoyable, though, and whilst there were a lot of tricky parts and I'm sure I lost quite a few marks, I think it went rather well, overall, so I'm feeling quite happy about it
#233 Re: Help Me ! » Definite integration (by parts) » 2011-06-18 23:00:59
Thanks everyone, I will certainly let you know how I get on.
#234 Re: Help Me ! » Definite integration (by parts) » 2011-06-18 07:22:21
Well that's very true. Thanks for the advice.
#235 Re: Help Me ! » Definite integration (by parts) » 2011-06-18 07:03:07
Thanks a lot .
No, I'm looking forward to it, to be honest, but I know I'm liable to make silly mistakes. Had I not finished C3 with half an hour to spare I would have dropped a lot of easy marks - for example when I accidentally added, rather than subtracting, when using the quotient rule.
#236 Re: Help Me ! » Definite integration (by parts) » 2011-06-18 06:54:33
Hmmm...I think it's more common with volume of revolution, but we'll see - I think it's more accuracy in general that I need to be careful with
#237 Re: Help Me ! » Definite integration (by parts) » 2011-06-18 06:29:13
Hmmm...Okay, thanks once again Bobbym - hopefully I won't do that in my C4 exam on Monday 
#238 Re: Help Me ! » Definite integration (by parts) » 2011-06-18 06:16:04
Oooooh thanks Bobbym - that's absolutely perfect. That has fixed it. However, I would like to confirm - does it matter whether I leave the limits out, or do it bit by bit. Will it always give the same result, or should I choose one method in preference of another?
#239 Re: Help Me ! » Definite integration (by parts) » 2011-06-18 06:05:39
Ooops - you're right, I have made a mistake there. Let me see if fixing that will solve my problem - thanks
#240 Re: Help Me ! » Definite integration (by parts) » 2011-06-18 05:42:45
Hi guys, so the question is:
My working - putting the limits in as I go is:
This gives the wrong answer; however, computing the antiderivative first and then simply adding the limits at the end does give the right answer.
My question, then, is this - should we add the limits in as we go as I have done here and then add them all up at the end, or save the limits until the end. One book does the former the other the latter and I have become quite confused . Thanks
#241 Help Me ! » Definite integration (by parts) » 2011-06-18 05:32:04
- Au101
- Replies: 22
Hi guys, I have a question regarding integration by parts over an interval. Suppose we have to integrate the following:
If we do this without limits we end up with:
My question is - when we do it between limits, should we have:
Which is how I was taught that this should be done and which gives:
Or, should we have:
Which is right and gives:
I'm confused, because i was always told to put limits in as I went - but that has given me the wrong answer. To avoid an overlong post, I shall post the exact question, with my working, in the next post. Perhaps I have made a mistake somewhere else.
#242 Re: Help Me ! » The Method of Differences » 2011-05-23 07:36:25
Oh I see, so it's intuition and recognition, over a hard-and-fast method. Well, I guess I feel a bit better now, it was just that the book confused me somewhat, by proposing something of a standard form and then just completely ignoring it.
Thank you ever so much, yet again:)
#243 Re: Help Me ! » The Method of Differences » 2011-05-23 07:23:45
Oh, okay I think I'm happier with it now. But I am now slightly more concerned. In this question its easy, but what about in instances where the differences aren't given and I have to derive them myself. If the form f(r) - f(r + 1) is flexible, then how do I know how to split my series up so that the differences cancel like that.
#244 Re: Help Me ! » The Method of Differences » 2011-05-23 07:08:50
Hehe A very good point, one which I'm becoming acutely aware of, because I am trying, myself, to put together a few notes. Not like a real textbook for publishing, or anything, but I've essentially been writing my own textbook so that when I forget all of this in about two years or something, I have something to look back on. And, I suppose, the first thing I want to do is to get a good explanation of the method of differences, because the whole
Definition doesn't seem to quite fit the bill and I'm not sure how else I can define the method, before I worry about trying specific examples.
#245 Re: Help Me ! » The Method of Differences » 2011-05-23 06:47:04
Hi, thanks bobbym.
Okay, I understand that, but I think this is what's confusing me - I felt that, since those two functions aren't of the form:
I was confused about my original definition of the method of differences, surely this needs to be refined? Apart from that, I think I see how your layout could be used, though, so that's one problem solved:). The layout which the book uses is very convoluted and - I don't mean to appear snobbish - but somehow ugly and messy and I quite like mathematical reasoning and I like to lay-out my solutions properly, but the alternative method which I found seemed to rely upon proving that relation, which isn't applicable here.
#246 Re: Help Me ! » The Method of Differences » 2011-05-23 06:31:42
Ooooh thanks for yet another swift reply bobbym. That's really nice, I understand that perfectly, but I am rather confused about questions like this:
I was able to show part (a) fine, but I struggle with part (b) because I don't believe that this expression can be put in the form:
Once more - thank you very much
#247 Help Me ! » The Method of Differences » 2011-05-23 06:09:25
- Au101
- Replies: 11
Hi guys,
I have a problem with the method of differences, in relation to series. I am given to believe that the method relies upon terms cancelling with the preceding or succeeding term and it is introduced in my textbook thus:
Which implies that the method only applies for series of this form - however, most of the questions which I have seem to involved series which are not, in fact, of this form. My first question, then, is basically if somebody could explain this method more thoroughly - preferably starting from the basics, but working-up to a rigorous 'professional' definition. The majority of my confusion, however, has arisen from my being unsure how to lay out answers to these questions, but I think it might be better to post specific question examples later.
Thanks
#248 Re: Help Me ! » Numerical Methods » 2011-04-17 23:37:03
Hmmm thank you very much both of you. I think I've got it now .
#249 Re: Help Me ! » Lemmas » 2011-04-17 23:30:04
Ooooh, that's good, thanks for the further examples .
#250 Help Me ! » Numerical Methods » 2011-04-17 11:27:05
- Au101
- Replies: 4
Hi guys, I have a question regarding how the iterative method actually works - I don't really understand the mathematical theory behind why it works and I would be really grateful if anybody could explain.
In C3 (Core Mathematics 3 - a British mathematics course studied when we are usually in our final year of pre-university education, or, sometimes our penultimate year) we are taught that:
"To solve an equation of the form:
By an iterative method, rearrange:
Into a form:
And use the iterative formula:
(From 'Heinemann Modular Mathematics for Edexcel AS and A-Level)
So, to exemplify how this works, a question may be something like:
(a) Show that the equation:
Can be arranged in the form:
,Stating the value of the constant q.
(b) Using the iteration formula:
With:
And the value of q found in part (a), find:
.Give the value of:
,To 4 decimal places.
Please note that I know how to do the question - I simply substitute 0.2 into the formula and then substitute the result back in until I reach the required result. My question is not about the question itself - I just thought that it might help you to understand the method, my question is why, mathematically, does this work. I don't understand why this formula should converge on the root of the equation.
If anybody can offer an explanation, I would, as ever, be very grateful .
Many thanks .