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The common function seems to go by the names bound and clamp. The simple ghit test suggests the former name, but that's polluted by such things as Python's bound methods. I don't mean for this to be a poll, but is there a (most-) standard convention of which I'm not aware? -- Tardis ( talk) 01:34, 15 October 2008 (UTC)
Does anybody know how to fund the conjugate harmonic function of this function:
I've been trying to solve it using maxima, but taking the x derivative and then integrating with respect to y and vice versa just leaves me with a horrible mess. is there some sort of trick involved?
Well, it's even simpler. The difficulty is mostly psychological, indeed. Let see. This is clearly an harmonic function from a textbook, not from the real mathematical world, as the simultaneous presence of the exponential and polynomial part indicates (in real life they would fight). Textbooks are supposed to be friendly, and didactic. So, what do they want to teach you? Most likely, a definition: v is conjugate to u iff u+iv is holomorphic. Can you figure out the whole thing, that is, the holomorphic? The polynomial is clearly half of a cube:
.
The exponential looks more difficult, but we are at the zoo, and it will not bite. So let's replace y-2 with y, as suggested by Dmcq, just to see it better (indeed, whoever invented this exercise, made a substitution of a with a as a last touch, because he thought it was too easy otherwise)... now, and are real and imaginary part of ; is the real part of ... remember, it has to be easy... Can you see it? why not ?
Yes, of course:
,
and you can see the u and v parts (and don't forget to replace y-2 where it was). You see? It's easy. Remember Kung Fu Panda. There is no secret ingredient. Just be confident! PMajer ( talk) 21:10, 16 October 2008 (UTC)
I just want to confirm that I've got the approach re future value correct.
If I want to calculate the future value of $1,000 with interest of 8% p.a. in 400 days, is it correct to calculate it like this?
Or do I have to convert the 8% p.a. rate to a rate over 400 days? —Preceding unsigned comment added by 203.3.186.10 ( talk) 03:19, 15 October 2008 (UTC)
Hmmmm. I'm not so sure because consider the exponent being 730/365 and then the result is the same as if you only earned simple interest (not compound) and the result is the same as 1.08*1.08 which is compound interest but only one period per year, thus you are only earning simple interest, but with 1 compounding point at the end of the 365th day. I have a ba in fin, and its confusing because we're expected to equally learn several different types of interest rates and conversions between them. The main thing which is lacking from your formula is e and/or ln, that's usually an indicator Interest rates by convention are always nominally quoted, usually twice per year, or yearly. So if the 8% is an effective interest rate, then I'd have to dig up my old book, but Gandalf is very smart, so he's probably correct. Sentriclecub ( talk) 21:36, 16 October 2008 (UTC)
Thanks everyone 203.3.186.10 ( talk) 07:12, 17 October 2008 (UTC)
Mathematics desk | ||
---|---|---|
< October 14 | << Sep | October | Nov >> | October 16 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
The common function seems to go by the names bound and clamp. The simple ghit test suggests the former name, but that's polluted by such things as Python's bound methods. I don't mean for this to be a poll, but is there a (most-) standard convention of which I'm not aware? -- Tardis ( talk) 01:34, 15 October 2008 (UTC)
Does anybody know how to fund the conjugate harmonic function of this function:
I've been trying to solve it using maxima, but taking the x derivative and then integrating with respect to y and vice versa just leaves me with a horrible mess. is there some sort of trick involved?
Well, it's even simpler. The difficulty is mostly psychological, indeed. Let see. This is clearly an harmonic function from a textbook, not from the real mathematical world, as the simultaneous presence of the exponential and polynomial part indicates (in real life they would fight). Textbooks are supposed to be friendly, and didactic. So, what do they want to teach you? Most likely, a definition: v is conjugate to u iff u+iv is holomorphic. Can you figure out the whole thing, that is, the holomorphic? The polynomial is clearly half of a cube:
.
The exponential looks more difficult, but we are at the zoo, and it will not bite. So let's replace y-2 with y, as suggested by Dmcq, just to see it better (indeed, whoever invented this exercise, made a substitution of a with a as a last touch, because he thought it was too easy otherwise)... now, and are real and imaginary part of ; is the real part of ... remember, it has to be easy... Can you see it? why not ?
Yes, of course:
,
and you can see the u and v parts (and don't forget to replace y-2 where it was). You see? It's easy. Remember Kung Fu Panda. There is no secret ingredient. Just be confident! PMajer ( talk) 21:10, 16 October 2008 (UTC)
I just want to confirm that I've got the approach re future value correct.
If I want to calculate the future value of $1,000 with interest of 8% p.a. in 400 days, is it correct to calculate it like this?
Or do I have to convert the 8% p.a. rate to a rate over 400 days? —Preceding unsigned comment added by 203.3.186.10 ( talk) 03:19, 15 October 2008 (UTC)
Hmmmm. I'm not so sure because consider the exponent being 730/365 and then the result is the same as if you only earned simple interest (not compound) and the result is the same as 1.08*1.08 which is compound interest but only one period per year, thus you are only earning simple interest, but with 1 compounding point at the end of the 365th day. I have a ba in fin, and its confusing because we're expected to equally learn several different types of interest rates and conversions between them. The main thing which is lacking from your formula is e and/or ln, that's usually an indicator Interest rates by convention are always nominally quoted, usually twice per year, or yearly. So if the 8% is an effective interest rate, then I'd have to dig up my old book, but Gandalf is very smart, so he's probably correct. Sentriclecub ( talk) 21:36, 16 October 2008 (UTC)
Thanks everyone 203.3.186.10 ( talk) 07:12, 17 October 2008 (UTC)