# Oxbridge Physics Prelims Revision

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Willa
ah okies (didnt realise his name was nicki though...awwww)
i'm gonna hope that was a type from chloé - if not, she should be glad we've got no more lectures this year! :vmad:
LennonMcCartney
Yes but analytic functions of real variables don't always map into the real numbers. That's my point, which is what you said below.

Yes they do or you have a different definition of analytic - analytic means defined, or capable of being defined, by a power series
RichE
Yes they do or you have a different definition of analytic - analytic means defined, or capable of being defined, by a power series

So isn't $f(x)=x^{-\frac{1}{2}}$ analytic? It can be represented by a power series, but $f(-1)$ does not belong in the set of Real numbers.
LennonMcCartney
So isn't $f(x)=x^{-\frac{1}{2}}$ analytic? It can be represented by a power series, but $f(-1)$ does not belong in the set of Real numbers.

but -1 won't be in the domain of any power series you choose to use to define x^(-1/2) - the domain being defined as within the radius of convergence of the power series
Anyway, I thought analytic could also mean infinitely differentiable.
RichE
but -1 won't be in the domain of any power series you choose to use to define x^(-1/2) - the domain being defined as within the radius of convergence of the power series

Ah yes good point. What about f(-0.5)?
LennonMcCartney
Anyway, I thought analytic could also mean infinitely differentiable.

the term for that is $C^\infty$ or "smooth"
LennonMcCartney
Ah yes good point. What about f(-0.5)?

well -0.5 wouldn't be in the domain either

what power series do you have in mind?
RichE
the term for that is $C^\infty$ or "smooth"

Ohhhh.... so smooth and analytic aren't identical properties of a function; now I get it. Thanks for clearing that up.
RichE
well -0.5 wouldn't be in the domain either

what power series do you have in mind?

And again a good point. I'm just being silly here.
LennonMcCartney
Ohhhh.... so smooth and analytic aren't identical properties of a function; now I get it. Thanks for clearing that up.

for a complex function to have a derivative on an open set is enough for it to be analytic (or holomorphic)

this isn't the case, even for smooth functions, with the real numbers

the function

f(x) = exp(-1/x^2) if x =/= 0 and f(0)=0

has derivatives of all orders at 0 and they are all 0

clearly it isn't analytic though because its Taylor series defines the zero function
Good shout. Cheers mate.
LennonMcCartney
Good shout. Cheers mate.

de rien - really I should apolologise for mathecising a physics thread
LennonMcCartney
No quaternions at all in our physics.

Fooking quaternions!
That's shiny's random comment of the day (:
LennonMcCartney
That's shiny's random comment of the day (:

wishful thinking - there will be others

what do you think of octonions shiny?
Bezza
i'm gonna hope that was a type from chloé - if not, she should be glad we've got no more lectures this year! :vmad:

maybe it's a sign of affection....or some other freudian slip

And nobody has answered my standard error query But I think it is that the standard error is the standard deviation divided by Root(N-1). But then what exactly is the root mean square deviation?
Bezza
i'm gonna hope that was a type from chloé - if not, she should be glad we've got no more lectures this year! :vmad:

Sorry!!!! It most certainly was a typo (rep coming your way!) as I was posting before I had to go to a tute (which has now been rearranged for tomorrow). Sorry NICK; I know how annoying it is as people keep calling me Cholé which is incrediably annoying..however possibly calling you a girl is worse! Sorry!!!
RichE
what do you think of octonions shiny?

dunno, never used them. but quaternions used to give me a headache when i did graphics programming especially if another library used matrix/vector notation and you had to convert between the two
Hoofbeat
Sorry!!!! It most certainly was a typo (rep coming your way!) as I was posting before I had to go to a tute (which has now been rearranged for tomorrow). Sorry NICK; I know how annoying it is as people keep calling me Cholé which is incrediably annoying..however possibly calling you a girl is worse! Sorry!!!

i didnt even name Cholé was a name? Or is that another typo (in which case you've completely confussled me)?